People who are building for the first time Vacation home independently, often get lost when marking the site. Indeed, drawing an angle on the ground or drawing a straight line is significantly more difficult than on paper - the scale is different. What complicates matters is that natural area it is never perfectly level and there are always landscape features that interfere with the measurement. However, the problem can be solved.
The markings are based on the principles of geometry, which originally served precisely this purpose: the word itself, translated from Greek, means “measurement of the earth.” So laying out angles on the ground is not a new thing, similar to drawing in school notebook. However, the difference is significant: a ruler and compass are used to construct a figure on paper, but they cannot be used on a real site.
How to construct a right angle on the ground
In this situation, a long reinforced thread or suitable twine (“clothesline”) will help out.
Straight lines and segments are built using thread. To do this, at the starting point, a peg is driven into the ground, to which one end of the thread is tied. Then the thread is pulled in the desired direction, in the case of constructing a segment - by specified length, pre-marked on the thread. At the resulting point, drive in a second peg and, pulling it tightly, tie a thread to it. If the twine is used only for measurement, then it makes sense to first apply a meter scale to it. To do this, every second meter is covered with black paint, preferably waterproof, and every fifth meter is covered with bright paint (for example, red). This “zebra” simplifies marking, allowing you to quickly measure long sections. Sometimes it makes sense to make the scale smaller by coloring every 50 or even 20 cm of twine.
If the terrain is very uneven, then it is better to use “suspended” markings, driving in pegs of different heights (Fig. 1, a). If the difference in height between the initial and end point is too large (the site is located on a steep slope), then the task becomes a little more complicated. You can use several pegs, adding up the distance between them. True, when marking in “steps”, you need to ensure that the angle between the peg and the rope remains straight. (Fig. 1, b).
In order to lay a right angle on the ground, you can use the principle of a triangle, where the sides are in a ratio of 3:4:5 (the so-called “ Pythagorean triple"). In this case, the triangle is right-angled, with angles of 90, 60 and 30 degrees. The smaller sides are legs, the angle between them is right.
In practice, the method is used in the following way. On the ground, from the starting point “0” (see Fig. 
2), marked with a peg, a straight line is drawn on which a 4-meter long segment is laid out - the side of the future angle (“a”). The end of the segment (point “1″) is marked with a peg. Then, a thread is tied to the starting peg, with a mark at a distance of exactly 3 meters from the peg, and laid by eye on the ground, approximately in the direction of the second side of the corner (“b”). From point 1 to the end of thread b, a thread is laid in the same way with a mark at 5 meters (“c”). Then threads b and c need to be taken into different hands, tighten as much as possible and in this state bring them together, precisely aligning the marks (point “2″). The result will be a triangle, where the “zero” angle will be right. For clarity, a schematic drawing is shown.
The lengths of the guide threads can be larger or smaller, but must be in a ratio of 4:3:5. Obviously, a right angle will always lie opposite larger side triangle.
Using the same method, you can easily set almost any angle divisible by 30 degrees by selecting the length of the guide threads. Here is the length ratio for some angles: 90 degrees (a = 4; b = 3; c = 5), 60 degrees (a = 3; b = 5; c = 4 or a = 5; b = 5; c = 6) , 30 degrees (a = 5; b = 4; c = 3), 120 degrees (a = 5; b = 5; c = 8)
How to correctly calculate a right angle
How to find a right angle of 90 degrees
How to find a 90 degree angle using a tape measure and a pencil?
Many builders have encountered this problem - how to find a 90-degree angle or how to find out whether an angle is obtuse (more than 90 degrees) or acute (less than 90 degrees).
Let’s not go back to school geometry and study tricky words, but let’s look at it in practice, where each person, literally in one minute, can determine how many degrees this or that angle has. And in 5 minutes, you can make an exact square with a right angle, that is, 90°.
Let's take for example.
On one side (on leg “a”) we measure 60 cm. Then on the other side (on leg “b”) we measure 80 cm. If from point “a” to point “b” the perpendicular “c” is 100 cm (1 meter ) means the angle is 90 degrees. If it is larger, for example 1.1 m, the angle is obtuse, and when it is 0.9 m, the angle is acute. Thus, with the help of a construction tape and a pencil, we were able to obtain a right angle.
Now let’s look at the numbers 60 and 80 and why the perpendicular should have 1 m. We take the combination of numbers “3,4,5” and multiply each number by our own invented number - for example, “5”.
3 (multiply) 5 = 15 legs
4*5=20 legs
5*5=25 hypotenuse
In the above example, we took the numbers “30, 40, 50” and multiplied each number by “2”, in this way we got the following combination:
30*2=60 legs
40*2=80 legs
50*2=100 hypotenuse
How to make a 45 degree angle using a tape measure and a pencil?
Before getting a 45 degree angle, use the system outlined above to make a right angle. Then, on the side “a” and “b” we measure the same dimensions and draw the hypotenuse. We measure the hypotenuse and divide by two (/2). Then we draw a line to the right angle. In this way we divided 90 degrees into 45 - two identical parts of 45°.
How to make a square with a right angle yourself in 5 minutes?
1 We connect two even wooden slats together, so that one of them is perpendicular to the other.
2 Then we measure two legs according to the above system.
3 Arrive the wooden slats to the first mark
4 We measure the hypotenuse and fix it on the second leg.
5 We check all dimensions and additionally fix them in all places.
6 Then cut off the excess parts.
How to find a right angle of 90 degrees video
How to make a right angle between walls.
The ancient Greek geometers and, in particular, Euclid, tried in vain; their knowledge never reached Soviet builders. In the sense that there are no rectangular rooms in Soviet houses. And there are in best case scenario in the form of a parallelogram, truncated trapezoid or rhombus, and in the worst and most common form in the form of an irregular quadrilateral. This quite often makes it difficult to achieve high-quality finishing of premises. You have to look for a right angle yourself. In general, this is not difficult to do.
The easiest way to mark is on the floor. For this you will need:
- Marker, chalk or pencil
- Construction level, string or construction cord.
- Roulette.
By using building level or a plumb line (easier - using a level, more precisely - using a plumb line) determine the protruding sections of the walls. In these places, transfer vertical marks to the floor. Draw straight lines through 2 marks along each wall so that the remaining marks (if you have them) remain between the line and the wall.
If the walls are perpendicular this distance should be equal to
1.414 m is more accurate than 1.41421356 m, but you won't need that much precision.
If the distance (the hypotenuse of the triangle) is greater, then instead of right angle between the walls is dull. In order to get a right angle, place the beginning of the tape measure at the point of intersection of the lines in the corner and draw a small arc with a radius of 1 m. Then attach the beginning of the tape measure to the mark on the line along the wall taken as a basis and draw a small arc with a radius of 1.414 m. Draw through the point of intersection arcs and the point of intersection of the lines in the corner of a straight line. This new line and will be the outline of the wall. If this is too difficult for you, then simply measure 1.414 m on the hypotenuse from the mark at the wall that you took as the basis. Draw a straight line through the resulting mark and the intersection point of the lines in the corner. In this case, you will not get a right angle, but still much closer to a right angle than the one you got.
How to calculate a right angle
If the lines forming an angle are drawn on paper, then you can determine that the angle is right, for example, using a protractor. Place it parallel to either side so that the zero mark coincides with the top of the corner. If the other side of the angle corresponds to the ninety-degree division of the protractor, then congratulations - you have determined that this particular angle is right. The same can be done using a square, and if absolute precision is not required, then even using other items at hand - matchbox, floppy disk, plastic CD/DVD box and any other rectangular object.
If in the conditions of the problem the lengths of the sides of a triangle are given, then you should determine the one that is the hypotenuse - the angle opposite it will be right. The hypotenuse is always the longest side of a right triangle, so there will be no problems with determining it in advance.
Marking the foundation for the house. Forum members say
If there are two of these, then the triangle is not rectangular and the angle you need does not exist in it at all. IN otherwise perform an additional check - the square of the length of the hypotenuse must be equal to the sum squares of the lengths of two short sides (legs). If this is so, then the angle opposite the long side (usually denoted by the letter γ) is right.
If you need to calculate the construction of a right angle, then perform the reverse operation described in the previous step. First, determine the lengths of the two sides that will form this angle. It's easier to work with the right one isosceles triangle, so it's better to take same lengths legs. If the result needs to be displayed on paper, then put the required length on a compass, put a point at the vertex of the future angle and designate it with the letter A. Draw a circle with the center at this point and draw a radius, marking the point of its tangency with the circle with the letter B. Then calculate the length of the hypotenuse - multiply the leg length by Square root from two. Put the resulting value on the compass and draw a second circle with the center at point B. Then connect the intersection point of the two circles (point C) with the center of the first circle (point A). This will be the right angle of YOU.
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Video lesson “Constructing right angles on the ground” is a video material that can be used by a teacher in a geometry lesson to familiarize himself with the methods of constructing angles on the ground. This material contains information about the device measuring tool- eker, as well as a detailed description of the method for measuring angles on the ground with this device. Material reveals practical use subject, connects geometry with spheres of human life.
We carry out precise marking of the foundation ourselves
This information creates greater interest in the subject of study and helps to better assimilate the educational material.
The use of video makes it possible to familiarize yourself with the device without resorting to additional equipment to demonstrate the device, its structure and principle of operation. When studying a topic of the same name, video material can become a teacher’s assistant, replacing his story about the structure and operation of the device with a visual one. detailed description with voice explanation. This material can also be recommended for self-study at in-depth study material, as well as simply supplement a geometry lesson or extracurricular activities in mathematics with cognitive information.
The video lesson begins with the announcement of the title of the topic “Constructing right angles on the ground.” The student is informed that to construct angles on the ground they use special devices. Among such devices, the simplest one is considered measuring device eker. The screen displays a drawn eker, which consists of two bars, the angle between which is 90°. This device is mounted on a tripod so that it can be taken sustainable position. The device is supplemented with nails driven into its bars so that the angle between the lines drawn through them will be right, that is, these lines are perpendicular to each other.
The construction of straight lines, the angle ∠AOB between which is 90°, begins with the correct location of the device. The ecker is installed in such a way that the plumb line located in its center is located directly above the point that is the vertex of the angle. The direction of one of the bars follows the direction of one side of the corner. Pin this direction possible by installing a milestone that records the passage of the OA side. To construct a right angle, a pole is also placed in the direction of the second block, fixing the direction of the straight line. In this way, a right angle is obtained, the construction of which is determined by the established milestones.
This device is imperfect, it is the simplest tool to construct angles on the ground, so students are shown a special device, the use of which is widespread in construction and architecture - a theodolite.
The video tutorial “Constructing right angles on the ground” is recommended as visual material to conduct a lesson on the same topic. It can also be used as a supplement to extracurricular activities in mathematics, for distance learning, For independent development material.
Typically, a straight line along one of the 2 widest walls is taken as the basis if there are no other reference points. In this case, the area of the room during further finishing will be reduced minimally.
Measure 1 m from one of the corners using a tape measure and place a mark on the line. Do the same on a (maybe not completely) perpendicular line.
Connect the resulting marks to form a triangle.
Measure the distance between the marks obtained.
If the walls are perpendicular, this distance should be ~ 1.414 m, more precisely 1.41421356 m, but you will not need such precision.
If the distance (the hypotenuse of the triangle) is greater, then instead of a right angle between the walls you have an obtuse one.
How to construct a right angle?
In order to get a right angle, place the beginning of the tape measure at the point of intersection of the lines in the corner and draw a small arc with a radius of 1 m. Then attach the beginning of the tape measure to the mark on the line along the wall taken as a basis and draw a small arc with a radius of 1.414 m. Draw through the point of intersection arcs and the point of intersection of the lines in the corner of a straight line. This new line will be the outline of the wall. If this is too difficult for you, then simply measure 1.414 m on the hypotenuse from the mark at the wall that you took as the basis. Draw a straight line through the resulting mark and the intersection point of the lines in the corner. In this case, you will not get a right angle, but still much closer to a right angle than the one you got.
If the distance (the hypotenuse of the triangle) is smaller, then instead of a right angle between the walls you have an acute one. In order to get a right angle, step back from the mark on the line along the wall, taken as a basis, a few centimeters. Draw small arcs on the floor according to the principle outlined in previous paragraph. The resulting line can be moved closer to the wall. The main condition is that the marks of the protruding sections of the wall must remain between the new line and the wall.
If you do not quite understand this text, then the picture will help you understand better:
From the obtained 2 sides of the rectangle using the method parallel transfer the remaining 2 sides are determined.
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What angle do the walls form? The first way is measurement.
To design furniture, we not only need to measure the length and height of the walls in an apartment or house, but we also need to measure the angle at which the furniture will be installed.
Why do you need to do this? - so that there are no problems with installation, to avoid huge side gaps, and so that the necessary adjustments can be made during production.
For example, a turned corner will not allow you to install a corner kitchen without additional undercuts of the internal corner modules and countertops. An acute corner can pull the exit of the furniture body beyond the installation dimensions, because it is impossible to install a furniture module flush into the corner.
Actually, when the reasons have been clarified and the need to measure the angle is obvious, the only thing left to do is measure the angle.
If you have a protractor in your home arsenal, then no problem, but if not, then the method described below will always come to the rescue.
The first thing you need to do is mark two points on the walls at the same level (at the height where the furniture module will be installed) as follows:
- From the corner, use a tape measure to measure along the left and right walls, for example, 500mm. and put points.
- Next, measure the diagonal - i.e. distance between points.
So, for example, we have three sizes - leg 500mm, 500mm. and diagonal 700mm.
The next stage is building a corner on a template from any material. In our case, I will show how to do this in the autocad program, but you can also do it with a compass, ruler, protractor and material for the template.
- Draw a horizontal segment of 500mm. with points "AB". (See drawing below.)
- Draw a circle with a radius of 500mm. with center at point "B".
- Draw a second circle with a radius of 700mm. with center at point "A".
- At the point of intersection of the circles we place point “C”.
- We connect points “B” and “C” with a segment and get our angle.
- Next, it remains to measure the angle with a protractor on the template or special tool in the autocad program. and use the existing drawing for design.
When the drawing is drawn, we can conclude that the measured angle is 89 degrees, the angle is acute and it will not be able to negatively affect the installation of furniture, because
How to accurately mark a right angle on the ground without a protractor?
1 degree is quite small.
What angle do the walls form? The second method is calculation.
- We measure 1000 mm from the corner (the more, the better - the error is smaller... of course, if you are using 400*400 mm for a shelf, then you don’t need to measure more than 400 mm) on both walls, and put marks (if you have wallpaper, you can use needles);
- We measure the distance between the marks (it’s better to do this together, again for reasons of accuracy), let’s say we get 1500 mm.
Those. For example, this is: (10002+ 10002– 15002) / (2 1000 1000) = -0.125 hence arccos (-0.125) = 97.18 degrees.
Supporting Information.
User Nastya Galkina asked a question in the Other education category and received 11 answers.
How to construct a right angle?
There is a method for constructing a right angle using a compass and ruler. First you need to draw a circle with a compass and draw its diameter. Then mark on the circle arbitrary point and connect it to the ends of the diameter: you get a triangle inscribed in a circle. Its angle (with its vertex at a point on the circle) will be right. The second way is to draw any two intersecting circles. Connect two intersection points with one line, and draw the other through the centers of the circles. These two segments will intersect at an angle of 90 degrees. If there are no drawing tools, you can use any rectangular objects. This can be a sheet of cardboard, any packaging (medicine, cigarette pack, box of chocolates, etc.), book, photo frame, etc.
How to construct a right angle using a compass and ruler
How to construct a right angle?
Before you learn how to construct a right angle, you need to remember its definition. A right angle is an angle of ninety degrees formed by two perpendicular lines. You can also say that it is half a full angle. There are several ways to construct a right angle.
Methods for constructing a right angle
The simplest thing is to construct a right angle using a drawing square. It is applied to the paper and lines are drawn along the perpendicular sides: a right angle is obtained. You can also use a protractor. Attach a protractor to the line drawn with a pencil and mark a ninety-degree angle on paper. Then connect this mark with a line (along a ruler) to a line on the paper.
There is a method for constructing a right angle using a compass and ruler. First you need to draw a circle with a compass and draw its diameter. Then mark an arbitrary point on the circle and connect it to the ends of the diameter: you get a triangle inscribed in the circle.
How to mark the foundation. DIY construction life hack
Its angle (with its vertex at a point on the circle) will be right. The second way is to draw any two intersecting circles. Connect two intersection points with one line, and draw the other through the centers of the circles. These two segments will intersect at an angle of 90 degrees. If you don't have drawing tools, you can use any rectangular objects. This can be a sheet of cardboard, any packaging (medicine, cigarette pack, box of chocolates, etc.), book, photo frame, etc.
Constructing right angles on the ground
In general, constructing right angles on the ground is necessary in construction, when dividing plots of land, etc. For this, special instruments are used - eker, astrolabe, theodolite. But it is unlikely that these tools will be, for example, on summer cottage. Then you can use a method that has been used since ancient times. You will need three pegs and ropes of 3, 4 and 5 meters. Stick a peg into the ground, tie 3 and 4 meter ropes to it, and the rest of the stakes to their ends. Connect the last two pegs with a 5-meter rope, pull the resulting triangle, and drive these stakes into the ground. The angle of the triangle with the first peg will be right.
As you can see, there are many simple ways to construct a right angle.
How to construct a right angle using a compass and ruler
How to construct an angle using a compass and ruler, knowing the tangent of this angle?
First, let's remember what a tangent is
Using a compass and a regular ruler (without divisions), we construct two perpendicular lines
Let's construct an angle whose tangent is equal to 2/3.
Let's measure an arbitrary segment with a compass and move it up two times from the intersection point, then to the left three times. Let us draw a ray through these points, as shown in the figure. The corner is built.
Let's construct an angle whose tangent equal to the root cubic out of three.
Let's find this number using a calculator
Let's round it down to a convenient value of 1.25 and write it in the form improper fraction 5/4. Similar to the previous method with Using a compass put five identical segments up and four to the left. WITH Using a ruler Let's pass a beam through them. The corner is built.
Let's construct an angle whose tangent is equal to Π .
And everything is the same as in the previous examples - 19 segments up and six to the left, connected - and the corner is built.
I would like to add that due to the fact that I slightly changed the values, the result of constructing the angles was Small error, but it will be invisible to the naked eye and even with the help of a protractor.
You can easily check - take a calculator
And about the correctness of constructing the angle according to the method that I indicated - using computer program We build angles according to the given parameters, then we build according to my method - we compare and make sure who is right and who is wrong. - more than a month ago
As you know, all these trigonometric quantities can be found from the ratio of the sides of a right triangle. In particular, the tangent of an angle is defined as the ratio of the length of the leg (side) lying opposite the given angle and the side adjacent to this angle. Therefore, the procedure will be as follows:
1) draw any straight line;
2) draw another line at right angles to it - to do this, use a compass to draw a circle of any radius with a center located on the first straight line, and then another circle of the same radius with a center located at the intersection point of the first circle and the first straight line; a straight line drawn through two points of intersection of these circles will be perpendicular to the first;
3) from the point of intersection of the first and second straight lines - the vertex of a right angle - we measure a segment of any suitable length on the first straight line, we consider that this is an adjacent leg;
4) knowing the ratio - tangent, we calculate the length of the second leg segment - the opposite one (multiply the tangent by the length of the first segment), and measure it from the same point / vertex on the second straight line;
5) connect all the vertices of the resulting right triangle, one of the angles of which, with the side on the first straight line, is the desired one.
FEBUS, I understand, it seems that you mean - with tgA = π the angle turns out to be close to 90 degrees, and if the tangent of the angle tends to infinity - then in general, the length of the ruler for constructing such a triangle should also be infinite. So what, exactly? The length of one leg will be 3.14 times greater than the length of the other - such a triangle can be constructed using the indicated method. What's wrong? - more than a month ago
Tangent is the ratio of the side opposite the angle to the side adjacent to the angle.
The tangent must be represented as a fraction of the numerator (this is the quantity opposite leg) and denominator (value adjacent leg)
Draw a straight line and draw a perpendicular to it; the intersection point is the vertex of a right angle (point A)
From the point of intersection (the vertices of a right angle - point A) on a straight line, you need to plot a segment, equal to the value opposite leg (point B).
On a straight line you need to plot a segment equal to the size of the adjacent leg (point C)
We connect points B and C to form triangle ABC
The tangent of angle ACB is equal to the known tangent.
Express it as a fraction tgA = π. - more than a month ago
To construct an angle with given value tangent of the angle, a compass is not needed, one ruler is enough.
In the coordinate system, we plot the unit along the abscissa axis (X), and the value of the tangent of the angle along the ordinate axis (Y). We connect a point with such coordinates to the origin of the coordinate system. The angle between the X axis and the constructed line is the desired angle.
Tangent = ratio of the opposite side to the adjacent side, i.e. tg (a) = Y/X.
I have X=1, which means tg (a) = Y. - more than a month ago
Let's start by defining what an angle is. Firstly, it is Secondly, it is formed by two rays, which are called the sides of the angle. Thirdly, the latter emerge from one point, which is called the vertex of the angle. Based on these characteristics, we can make a definition: angle - geometric figure, which consists of two rays (sides) emerging from one point (vertex).
They are classified by degree value, by location relative to each other and relative to the circle. Let's start with the types of angles according to their magnitude.
There are several varieties of them. Let's take a closer look at each type.
There are only four main types of angles - straight, obtuse, acute and straight angles.
Straight
It looks like this:
His degree measure always makes 90 o, in other words, a right angle is an angle of 90 degrees. Only such quadrilaterals as square and rectangle have them.
Blunt
It looks like this:
The degree measure is always more than 90 o, but less than 180 o. It can be found in quadrilaterals such as a rhombus, an arbitrary parallelogram, and in polygons.
Spicy
It looks like this:
The degree measure of an acute angle is always less than 90°. It is found in all quadrilaterals except the square and any parallelogram.
Expanded
The unfolded angle looks like this:
It does not occur in polygons, but is no less important than all the others. A straight angle is a geometric figure whose degree measure is always 180º. You can build on it by drawing one or more rays from its top in any direction.
There are several other minor types of angles. They are not studied in schools, but it is necessary to at least know about their existence. Minor species There are only five corners:
1. Zero
It looks like this:
The name of the angle itself already indicates its size. Its internal area is 0°, and the sides lie on top of each other as shown in the figure.
2. Oblique
An oblique angle can be a straight angle, an obtuse angle, an acute angle, or a straight angle. Its main condition is that it should not be equal to 0 o, 90 o, 180 o, 270 o.
3. Convex
Convex angles are zero, straight, obtuse, acute and straight angles. As you already understood, the degree measure convex angle- from 0 o to 180 o.
4. Non-convex
Angles with degree measures from 181° to 359° inclusive are non-convex.
5. Full
A complete angle is 360 degrees.
These are all types of angles according to their magnitude. Now let's look at their types according to their location on the plane relative to each other.
1. Additional
That's two acute angles, forming one straight line, i.e. their sum is 90 o.
2. Adjacent
Adjacent angles are formed if a ray is passed through the unfolded angle, or rather through its vertex, in any direction. Their sum is 180 o.
3. Vertical
Vertical angles are formed when two straight lines intersect. Their degree measures are equal.
Now let's move on to the types of angles located relative to the circle. There are only two of them: central and inscribed.
1. Central
A central angle is an angle with its vertex at the center of the circle. Its degree measure is equal to the degree measure of the smaller arc subtended by the sides.
2. Inscribed
An inscribed angle is an angle whose vertex lies on a circle and whose sides intersect it. Its degree measure is equal to half the arc on which it rests.
That's it for the angles. Now you know that in addition to the most famous ones - acute, obtuse, straight and deployed - there are many other types of them in geometry.
Those who are engaged in independent construction know that before the construction of a structure begins, they must mark out the foundation with their own hands. Here we consider the case of the start of work on the construction of a pile screw foundation on a site for a number of horticultural reasons not cleared of useful plants. This made it difficult to work on marking the future foundation, but these difficulties were easily overcome with the help of a simple device for setting right angles.
How to mark the foundation with your own hands
Typically, marking the foundation in self-construction is done by eye using a tape measure. First, posts marking the corners of the walls are placed at distances of the length and width of the future building. Then the diagonals of the resulting rectangle are measured and the process of rearranging two adjacent pillars begins until the diagonal measurements are aligned. According to the basics of geometry, a rectangle is a figure whose two diagonals are equal to each other. But it was precisely because of the fit that measuring the diagonals during the fitting process was difficult. Landings made it difficult to tighten the tape measure and obscured the rangefinder laser. But this difficulty can be overcome.
1. Before starting work, you must have minimal knowledge of geometry and know the solution to the Pythagorean theorem :). Let me remind you of the theorem. The square of the hypotenuse is equal to the sum of the squares of the legs in a right triangle.
2. Stretch a cord between two pegs indicating the first wall of the foundation. If the side of the foundation, for example, is 6 meters, then the distance between the pegs should be at least 8 meters.
3. Let's make a device for setting a right angle on the ground. To do this, you must purchase packaging. non-stretchy cord or use a steel cable. In total you will need about 13 meters of cord.
4. We tie the ends of the cord folded together so that the length of the resulting loop is 6 meters. Accuracy in tying and sizing is important.
5. Take a permanent felt-tip pen and, using a tape measure, make marks from the center of the knot at a distance of 3 meters in one direction and at a distance of 4 meters in the other direction. So we got rope right triangle. This invention will allow you to calculate the direction of a 90° angle by simply stretching the triangle.
Marking the first wall
Life hack kit
Sides of a triangle
6. To work on the ground, we will need thin wooden pegs or pieces of thin reinforcement.
7. We install one peg to indicate the corner of the foundation on the marking line made earlier in step 2.
8. Take a rope life hack. We place the knot on the peg indicating the angle and stretch the sides of the rope triangle by driving the first peg at a distance of 4 meters into the wall markings of step 2. The bend of the cord should be at the marker mark of 4 meters.
9. Place the peg at the 3 meter mark. One side of the rectangle is parallel to the marking of the first wall, and the second side indicates the direction of the marking at a 90° angle for the second wall. Pythagorean theorem in action - see photo.
Pieces of reinforcement
Right angle base peg
Rope triangle
10. We stretch the marking cord for the second wall, parallel to the side of the triangle.
11. We carry out similar actions to mark the third wall.
12. We mark the lengths of the second and third walls on the markings and carry out control at one of the angles of the correct direction of the fourth wall. If the length of the wall in the markings was 6 meters and its direction crossed the marking points of walls two and three, then we can say that measuring the diagonals will give an equal result. If alignment does not work, check again that the markings are installed correctly.
Marking the 2nd wall
This - oldest geometric problem.
Step-by-step instruction
1st method. - Using the “golden” or “Egyptian” triangle. The sides of this triangle have the aspect ratio 3:4:5, and the angle is strictly 90 degrees. This quality was widely used by the ancient Egyptians and other ancient cultures.
Ill.1. Construction of the Golden or Egyptian Triangle
- We manufacture three measurements (or rope compasses - a rope on two nails or pegs) with lengths 3; 4; 5 meters. The ancients often used the method of tying knots with equal distances between them. Unit of length - " nodule».
- We drive a peg at point O and attach the measure “R3 - 3 knots” to it.
- We stretch the rope along known border– towards the intended point A.
- At the moment of tension on the border line - point A, we drive in a peg.
- Then - again from point O, stretch the measure R4 - along the second border. We don’t drive the peg in yet.
- After this, we stretch the measure R5 - from A to B.
- We drive a peg at the intersection of measurements R2 and R3. - This desired point IN - third vertex of the golden triangle, with sides 3;4;5 and with a right angle at point O.
2nd method. Using a compass.
The compass may be rope or pedometer. Cm:
Our compass pedometer has a step of 1 meter.
Ill.2. Compass pedometer
Construction - also according to Ill. 1.
- From the reference point - point O - the neighbor's corner, draw a segment of arbitrary length - but larger than the radius of the compass = 1m - in each direction from the center (segment AB).
- We place the leg of the compass at point O.
- We draw a circle with radius (compass step) = 1 m. It is enough to draw short arcs - 10-20 centimeters each, at the intersection with the marked segment (through points A and B). With this action we found equidistant points from the center- A and B. The distance from the center does not matter here. You can simply mark these points with a tape measure.
- Next you need to draw arcs with centers at points A and B, but several (arbitrarily) larger radius, than R=1m. You can reconfigure our compass to a larger radius if it has an adjustable pitch. But for such a small current task I wouldn’t want to “pull” it. Or when there is no adjustment. Can be done in half a minute rope compass.
- We place the first nail (or the leg of a compass with a radius greater than 1 m) alternately at points A and B. And draw two arcs with the second nail - in a taut state of the rope - so that they intersect with each other. It is possible at two points: C and D, but one is enough - C. And again, short serifs at the intersection at point C will suffice.
- Draw a straight line (segment) through points C and D.
- All! The resulting segment, or straight line, is exact direction on North:). Sorry, - at a right angle.
- The figure shows two cases of boundary discrepancy across a neighbor's property. Ill. 3a shows a case where a neighbor’s fence moves away from the desired direction to its detriment. On 3b - he climbed onto your site. In situation 3a, it is possible to construct two “guide” points: both C and D. In situation 3b, only C.
- Place a peg at corner O, and a temporary peg at point C, and stretch a cord from C to the rear boundary of the site. - So that the cord barely touches peg O. By measuring from point O - in direction D, the length of the side according to the general plan, you will get a reliable rear right corner of the site.
Ill.3. Constructing a right angle - from the neighbor’s angle, using a compass-pedometer and a rope compass
If you have a compass-pedometer, then you can do without rope altogether. In the previous example, we used the rope one to draw arcs of a larger radius than those of the pedometer. More because these arcs must intersect somewhere. In order for the arcs to be drawn with a pedometer with the same radius - 1m with a guarantee of their intersection, it is necessary that points A and B are inside the circle with R = 1m.
- Then measure these equidistant points roulette- V different sides from the center, but always along line AB (neighbor’s fence line). The closer points A and B are to the center, the farther from it the guide points: C and D, and the more more accurate measurements. In the figure, this distance is taken to be about a quarter of the pedometer radius = 260mm.
Ill.4. Constructing a right angle using a pedometer and tape measure
- This scheme of actions is no less relevant when constructing any rectangle, in particular the contour of a rectangular foundation. You will receive it perfect. Its diagonals, of course, need to be checked, but isn't the effort reduced? – Compared to when the diagonals, corners and sides of the foundation contour are moved back and forth until the corners meet..
Actually, we decided geometric problem on the ground. To make your actions more confident on the site, practice on paper - using a regular compass. Which is basically no different.
A right angle between walls is necessary quite often. For example, to correctly install a bathtub, kitchen sink or table. But most people simply do not take this need into account, and then regret it when a centimeter gap appears between the bathtub and the wall. Also, an indirect angle is revealed by floor tiles when the cutting on the sides is different. And there are even worse situations. Therefore, treat this material in all seriousness.
Builders erecting modern houses, contrary to the opinion of the majority, they do not care about the proximity of the corners in apartments to 90 degrees. All they care about is the amount of work, and often they are not even given any measuring equipment. Just a trowel and a trowel. “Way, Rovshan!”
How to make a right angle between the walls after such a hack? There are two options here: either we plaster on the beacons, or we level the walls with plasterboard. And if in the second case no difficulties should arise - we just twist the profiles along the square, then everything is a little more complicated. By the way, the option “I’ll level everything with tiles” won’t work either. Practice shows that all those who try to make a right angle by smoothly building up a layer of tile adhesive invariably mess up. Moreover, their angle is not straight, and the tiles lie crooked. If you find the strength and courage to plaster on beacons, then you can make a perfect right angle without any problems. On which you can quite calmly lay the tiles “under the comb”.
First fundamental principle plaster at a right angle - first we plaster one wall in the usual way.
Usually the longest. Entirely. It is much easier and faster to build an angle from a finished plane.
What's next? You will need two plastering rules. Preferably the length of the entire wall. Often bathrooms have dimensions around 175x175, so in this case, take two two-room apartments and shorten them with a grinder or a hacksaw.
Let's assume that you have already plastered one wall, ideally. And the adjacent one has dimensions of 175x275 cm. In this case, two beacons will be needed. Let's mark them. Everything is as it should be, at a distance of 30 cm from the walls. But there's one here important nuance. The pair of lower screws must be strictly at the same level. Accordingly, the top pair too. A little later you will find out why. It is also recommended to mark a line on the plastered wall that lies at the same level as the bottom pair of screws.
Next, holes are drilled and dowels and screws are driven into them. Now what? Of course, you can’t do anything with a simple half-meter square. The solution lies on the surface - you need a larger square. It is made from two rules. But how to make sure that they form a strictly 90 degree angle? Not on a small square, that makes no sense. Everything is much simpler.
There is the Pythagorean theorem. Which unambiguously establishes the ratio of the sides of a right triangle. Root of the sum of squares of the legs equal to the hypotenuse. Remember school course geometry. What this all means is that if you can build a triangle on the floor whose sides are related in the same way, one of its angles will be exactly 90 degrees. The simplest case is the so-called. Egyptian triangle, whose sides are in a ratio of 3:4:5. It is usually convenient to take 120:160:200 cm in practice.
So, a line is drawn on the floor with a pencil. It is not advisable to use a marker; accuracy is important here. Two points are placed on it: one at the edge, the second at a distance of 120 cm from the first. Then take a piece of the lighthouse, or you can use a tape measure. It will be necessary to set aside 160 cm from the first point, and 200 cm from the second. More precisely, construct fragments of circles specified radii. The intersection point of these figures will be the third vertex of the triangle. All that remains is to connect the vertices. That's it, you have constructed a right triangle with high accuracy. 
The next step is to place two rules on the floor exactly along the lines. Since they will lie with their beveled edges facing outward, this will not be so easy. You'll have to use a square. So, the rules are combined with the lines: 
Now you need to securely fasten them together. This is usually done with self-tapping screws with a press washer or black metal screws. The main thing is to prevent the rules from shifting relative to the lines under the influence of vibration from a screwdriver or drill. It is enough to consolidate the rules at two points:
But, in general, this is not enough. You need to use an additional strip from a Knauf protective corner, for example. We fasten it as shown in the figure:
Now you have a huge, hard, and most importantly, accurate square. You return to the room where you will have beacons. There is already a line marked along which you will apply the square. Yes, you need to place it strictly in a horizontal plane, otherwise there will be an error.
You should have already previously assessed the degree of deviation of the angle from 90 degrees, so you know which screw from the bottom pair to take as a basis. Let's assume that the angle was obtuse, so the screw closest to the already plastered wall is unscrewed to a minimum (7-8 mm). And the far one will already twist around the square. Apply it to the line on the already finished wall and to the exposed screw of the bottom pair on the marked one. Look. Let's say the farthest self-tapping screw does not reach the square by about 4 mm. Unscrew it approximately this distance and again assess the situation with a square. You may have to apply it several times, but, in general, the installation process of the self-tapping screw will take you no more than a couple of minutes. If the angle was initially sharp, install the farthest self-tapping screw first. And the neighbor - along the square.
It is inconvenient to set the top pair of screws with the same square - it is heavy, it is difficult to lift it, it constantly slides off the heads. Therefore, it will be easier to simply set them vertically relative to the bottom pair. By plumb line or bubble level. In any case, if your first wall is perfectly aligned, you will get a perfectly right angle both above and below, automatically.
If you need to set a right angle on the opposite wall, then no problem, do everything exactly the same. This may be necessary, for example, if the dimensions of the bathtub are close to the walls. At the same time, cutting the tiles on the floor will work out perfectly. It is recommended not to place all the beacons in advance and then plaster them. It would be much better, although it would take longer, to mark and plaster each wall one by one. But you will know for sure that you have not made a mistake anywhere.
Now you know how to make a right angle between walls when plastering. By spending a couple of hours marking, you will save more on laying tiles, and get professional quality it will be much easier.
Jun 6, 2014 ADMIN