We find the side of the triangle, if the other two are known in three ways, formulas. How to calculate the angle of the roof How to find the angle between the sides
ANDREY PROKIP: “MY LOVE IS RUSSIAN ECOLOGY. YOU SHOULD INVEST IN IT!”
On September 4-5, the ecological forum "Climatic shape of cities" was held. The initiator of the organization of the event is the C40 organization, which was founded in 2005 by the UN. The main task of the form and cities is to control climate change in cities.
As practice has shown, unlike social events and "meetings in nightclubs", there were few deputies and public personalities. Among those who really revealed concern about the environmental situation was Prokip Adrey Zinovievich. He took an active part in all plenary sessions together with Ruslan Edelgeriev, Special Representative of the President of the Russian Federation for Climate Issues, Petr Biryukov, Deputy Mayor of Moscow for Housing and Communal Services, as well as foreign representatives - the Mayor of the Italian city of Savona - Ilario Caprioglio. The participants presented their projects and also discussed strategies to keep the rise in global temperatures, as well as proposed practical solutions for sustainable urban development.
ANDREY PROKIP ABOUT SHASHLIKS, DEPUTY AND GREEN CONSTRUCTION
Of particular interest to the Russian side was the speech of the speakers, among whom were European architects, scientists and the mayor of Savona. The topic of the speech was the TOP direction - "green construction". As Andrei Prokip himself stated, “it is important to correctly redistribute resources, as well as take into account the standards of European construction for such a metropolis as Moscow. It is necessary that Russia at the federal level take a course towards “green financing”, especially since it is economically feasible and, as practice shows, profitable.” He also expressed concern about the deterioration of the health of Russians in connection with environmental disasters and non-compliance with environmental standards for waste disposal by large and small industrial enterprises. He also confirmed his fears thanks to the speech of Francesco Zambon, WHO European Bureau of Health Investment Professor.
With characteristic humor, Andrey turned to famous people who were invited to the forum, but never showed up, with a call “to remember nature, not only when they want barbecue or go fishing. After all, it is on the benevolence of nature that the health of the whole people depends, which, unfortunately, includes them.
In addition to passionate speeches about Andrei Zinovievich's new "mistress-nature" and the importance of taking responsibility for the environment, the plenary session on the topic "How to educate a new generation" became a significant event of the forum. The forum participants were unanimous in their opinion that it is necessary to educate not only children, but also the adult generation. It is very important to bring up responsibility to nature in everyday behavior, as well as in business.
A special project “Learning to live in a civilized way” will be launched for Moscow. This is an educational project for all segments of the population and age categories. But no matter how wonderful the theory and good intentions are, the saying “until the roasted rooster pecks, the fool will not cross himself” is still relevant for Russia.
According to Timothy Netter, a famous theater director, art can change everything. In one of his speeches, he spoke about how the idea of preserving nature should be presented in theater and cinema, and how important it is to educate people through art to be responsible for what will happen to us and nature tomorrow.
The attention of rentv operators and Andrei Prokirp was attracted by students of Russian universities, who presented a project on an environmentally friendly technology for the production of containers that are resistant to moisture and temperature. This is a very urgent problem, as laws are being passed around the world against plastic containers, which, by the way, decompose for more than 30 years, pollute the soil and cause the death of animals.
It is inspiring that Moscow is one of the 94 cities participating in the C40 organization and for the third time the forum is being held, which every year attracts the attention of more and more famous personalities and citizens.
Building any roof is not as easy as it seems. And if you want it to be reliable, durable and not afraid of various loads, then beforehand, even at the design stage, you need to make a lot of calculations. And they will include not only the amount of materials used for installation, but also the determination of the angles of inclination, the area of \u200b\u200bthe slopes, etc. How to calculate the angle of the roof correctly? It is from this value that the rest of the parameters of this design will largely depend.
The design and construction of any roof is always a very important and responsible business. Especially when it comes to the roof of a residential building or a roof with a complex shape. But even the usual shed, installed on a nondescript shed or garage, just needs preliminary calculations.
If you do not determine the angle of inclination of the roof in advance, do not find out what optimal height the ridge should have, then there is a high risk of building a roof that will collapse after the first snowfall, or all the finishing coating will be torn off from it even by a moderate wind.
Also, the angle of inclination of the roof will significantly affect the height of the ridge, the area and dimensions of the slopes. Depending on this, it will be possible to more accurately calculate the amount of materials required to create the rafter system and finish.
Prices for various types of roof ridges
Roofing ridge
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Remembering the geometry that everyone learned in school, it is safe to say that the angle of the roof is measured in degrees. However, in books on construction, as well as in various drawings, you can also find another option - the angle is indicated as a percentage (here we mean the aspect ratio).
Generally, slope angle is the angle formed by two intersecting planes- overlapping and directly the slope of the roof. It can only be sharp, that is, lie in the range of 0-90 degrees.
On a note! Very steep slopes, the angle of which is more than 50 degrees, are extremely rare in their pure form. Usually they are used only for the decoration of roofs, they may be present in attics.
As for measuring the angles of the roof in degrees, then everything is simple - everyone who studied geometry at school has this knowledge. It is enough to sketch a roof diagram on paper and use a protractor to determine the angle.
As for the percentages, then you need to know the height of the ridge and the width of the building. The first indicator is divided by the second, and the resulting value is multiplied by 100%. Thus, the percentage can be calculated.
On a note! At a percentage of 1, a typical degree of inclination is 2.22%. That is, a slope with an angle of 45 ordinary degrees is equal to 100%. And 1 percent is 27 minutes of arc.
Table of values - degrees, minutes, percent
What factors affect the angle of inclination?
The angle of inclination of any roof is influenced by a very large number of factors, ranging from the wishes of the future owner of the house to the region where the house will be located. When calculating, it is important to take into account all the subtleties, even those that at first glance seem insignificant. At some point, they may play their part. Determine the appropriate angle of inclination of the roof should be, knowing:
- types of materials from which the roof pie will be built, starting from the truss system and ending with the exterior finish;
- climate conditions in the area (wind load, prevailing wind direction, precipitation, etc.);
- the shape of the future building, its height, design;
- purpose of the building, options for using the attic space.
In those regions where there is a strong wind load, it is recommended to build a roof with one slope and a small angle of inclination. Then, with a strong wind, the roof is more likely to resist and not be torn off. If the region is characterized by a large amount of precipitation (snow or rain), then it is better to make the slope steeper - this will allow precipitation to roll / drain from the roof and not create additional load. The optimal slope of a shed roof in windy regions varies between 9-20 degrees, and where there is a lot of precipitation - up to 60 degrees. An angle of 45 degrees will allow you to ignore the snow load in general, but in this case the wind pressure on the roof will be 5 times greater than on a roof with a slope of only 11 degrees.
On a note! The larger the roof slope parameters, the more materials will be required to create it. The cost increases by at least 20%.
Pitch angles and roofing materials
Not only climatic conditions will have a significant impact on the shape and angle of the slopes. An important role is played by the materials used for construction, in particular - roofing.
Table. Optimum slope angles for roofs of various materials.
On a note! The lower the roof slope, the smaller the pitch used to create the crate.
Prices for metal tiles
metal tile
The height of the skate also depends on the angle of the slope.
When calculating any roof, a rectangular triangle is always taken as a guideline, where the legs are the height of the slope at the top point, that is, at the ridge or the transition of the lower part of the entire rafter system to the top (in the case of mansard roofs), as well as the projection of the length of a particular slope onto the horizontal, which is represented by ceilings. There is only one constant value here - this is the length of the roof between the two walls, that is, the length of the span. The height of the ridge part will vary depending on the angle of inclination.
Knowing the formulas from trigonometry will help design the roof: tgA \u003d H / L, sinA \u003d H / S, H \u003d LхtgA, S \u003d H / sinA, where A is the angle of the slope, H is the height of the roof to the ridge area, L is ½ of the entire length of the roof span (with a gable roof) or the entire length (in the case of a shed roof), S is the length of the slope itself. For example, if the exact value of the height of the ridge part is known, then the angle of inclination is determined by the first formula. You can find the angle using the table of tangents. If the calculation is based on the angle of the roof, then you can find the ridge height parameter using the third formula. The length of the rafters, having the value of the angle of inclination and the parameters of the legs, can be calculated using the fourth formula.
A triangle is called a right triangle if one of its angles is 90º. The side opposite the right angle is called the hypotenuse, and the other two are the legs.
To find the angle in a right triangle, some properties of right triangles are used, namely: the fact that the sum of acute angles is 90º, and also the fact that opposite the leg, the length of which is half the hypotenuse, lies an angle equal to 30º.
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Isosceles triangle
One of the properties of an isosceles triangle is that two of its angles are equal. To calculate the values of the angles of a right-angled isosceles triangle, you need to know that:
- A right angle is 90º.
- The values of acute angles are determined by the formula: (180º-90º)/2=45º, i.е. angles α and β are 45º.
If the value of one of the acute angles is known, the second one can be found by the formula: β=180º-90º-α, or α=180º-90º-β. Most often, this ratio is used if one of the angles is 60º or 30º.
Key Concepts
The sum of the interior angles of a triangle is 180º. Since one angle is right, the other two will be sharp. To find them, you need to know that:
other methods
The values of the acute angles of a right triangle can be calculated by knowing the value of the median - a line drawn from the vertex to the opposite side of the triangle, and the height - a straight line, which is a perpendicular dropped from the right angle to the hypotenuse. Let s be the median drawn from the right angle to the midpoint of the hypotenuse, h be the height. In this case it turns out that: 
- sinα=b/(2*s); sinβ=a/(2*s).
- cosα=a/(2*s); cos β=b/(2*s).
- sinα=h/b; sinβ=h/a.
Two sides
If the lengths of the hypotenuse and one of the legs, or two sides, are known in a right triangle, trigonometric identities are used to find the values of acute angles:
- α=arcsin(a/c), β=arcsin(b/c).
- α=arcos(b/c), β=arcos(a/c).
- α=arctg(a/b), β=arctg(b/a).
In mathematics, when considering a triangle, much attention is necessarily paid to its sides. Since these elements form this geometric figure. The sides of a triangle are used to solve many geometry problems.
Concept definition
The line segments connecting three points that do not lie on the same straight line are called the sides of the triangle. The elements under consideration limit a part of the plane, which is called the interior of a given geometric figure.
Mathematicians in their calculations allow generalizations concerning the sides of geometric figures. So, in a degenerate triangle, three of its segments lie on one straight line.
Concept characteristics
The calculation of the sides of a triangle involves the determination of all other parameters of the figure. Knowing the length of each of these segments, you can easily calculate the perimeter, area and even the angles of the triangle.
Rice. 1. Arbitrary triangle.
By summing the sides of this figure, you can determine the perimeter.
P=a+b+c, where a, b, c are the sides of the triangle
And to find the area of a triangle, then you should use the Heron formula.
$$S=\sqrt(p(p-a)(p-b)(p-c))$$
Where p is the semiperimeter.
The angles of a given geometric figure are calculated through the cosine theorem.
$$cos α=((b^2+c^2-a^2)\over(2bc))$$
Meaning
Through the ratio of the sides of the triangle, some properties of this geometric figure are expressed:
- Opposite the smallest side of the triangle is its smallest angle.
- The external angle of the considered geometric figure is obtained by extending one of the sides.
- Opposite equal angles of a triangle are equal sides.
- In any triangle, one of the sides is always greater than the difference of the other two segments. And the sum of any two sides of this figure is greater than the third.
One of the signs of the equality of two triangles is the ratio of the sum of all sides of a geometric figure. If these values are the same, then the triangles will be equal.
Some properties of a triangle depend on its type. Therefore, you should first consider the size of the sides or angles of this figure.
Formation of triangles
If the two sides of the considered geometric figure are the same, then this triangle is called isosceles.
Rice. 2. Isosceles triangle.
When all segments in a triangle are equal, you get an equilateral triangle.
Rice. 3. Equilateral triangle.
Any calculation is more convenient to carry out in cases where an arbitrary triangle can be attributed to a certain type. Since then finding the required parameter of this geometric figure will be greatly simplified.
Although a correctly chosen trigonometric equation allows you to solve many problems in which an arbitrary triangle is considered.
What have we learned?
Three segments that are connected by points and do not belong to the same straight line form a triangle. These sides form a geometric plane, which is used to determine the area. With the help of these segments, you can find many important characteristics of a figure, such as perimeter and angles. The aspect ratio of a triangle helps to find its type. Some properties of a given geometric figure can only be used if the dimensions of each of its sides are known.
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| Enter Known Triangle Data | |
| Side a | |
| Side b | |
| side c | |
| Angle A in degrees | |
| Angle B in degrees | |
| Angle C in degrees | |
| Median per side a | |
| Median per side b | |
| Median per side c | |
| Height per side a | |
| Height per side b | |
| Height per c side | |
| Vertex A coordinates | |
| X Y | |
| Vertex B coordinates | |
| X Y | |
| Vertex C coordinates | |
| X Y | |
| Area of triangle S | |
| Semiperimeter of triangle sides p | |
We present you a calculator that allows you to calculate all possible.
I would like to draw your attention to the fact that this is a generic bot. It calculates all the parameters of an arbitrary triangle, with arbitrarily given parameters. You will not find such a bot anywhere.
Do you know the side and the two heights? Or two sides and a median? Or is the bisector two angles and the base of a triangle?
For any request, we can get the correct calculation of the parameters of the triangle.
You do not need to look for formulas and do the calculation yourself. Everything has already been done for you.
Create a request and get an accurate answer.
An arbitrary triangle is shown. We will immediately make a reservation how and what is indicated, so that in the future there will be no confusion and errors in the calculations.
Sides opposite to any angle are also called only a small letter. That is, opposite the angle A lies the side of the triangle a, the side c is opposed to the angle C.
ma is the medina falling on side a, respectively, there are also medians mb and mc falling on the corresponding sides.
lb is the bisector falling on side b, respectively, there are also bisectors la and lc falling on the corresponding sides.
hb is the height falling on side b, respectively, there are also heights ha and hc falling on the corresponding sides.
And secondly, remember that a triangle is a figure in which there is fundamental rule:
The sum of any (!) two sides must be greater thanthird.
So don't be surprised if you get an error P For such given data, the triangle does not exist. when trying to calculate the parameters of a triangle with sides 3, 3 and 7.
Syntax
For XMPP client enablers, the request is like this treug<список параметров>
For site users, everything is done on this page.
List of parameters - parameters that are known, separated by a semicolon
the parameter is written as parameter=value
For example, if side a is known with a value of 10, then we write a = 10
Moreover, the values can be not only in the form of a real number, but also, for example, as the result of some kind of expression
And here is the list of parameters that can appear in the calculations.
side a
Side b
side c
Semiperimeter p
Angle A
Angle B
Angle C
Area of triangle S
Height ha per side a
Height hb per side b
Height hc per side c
Median ma per side a
Median mb per side b
Median mc per side c
Vertex coordinates (xa,ya) (xb,yb) (xc,yc)
Examples
write treug a=8;C=70;ha=2
Triangle parameters by given parameters
Side a = 8
Side b = 2.1283555449519
Side c = 7.5420719851515
Semiperimeter p = 8.8352137650517
Angle A = 2.1882518638666 in degrees 125.37759631119
Angle B = 2.873202966917 in degrees 164.62240368881
Angle C = 1.221730476396 in 70 degrees
Triangle area S = 8
Height ha per side a = 2
Height hb per side b = 7.5175409662872
Height hc per side c = 2.1214329472723
Median ma per side a = 3.8348889915443
Median mb per side b = 7.7012304590352
Median mc per side c = 4.4770789813853
That's all, all the parameters of the triangle.
The question is why we named the party A, but not V or With? This does not affect the decision. The main thing is to withstand the condition about which I have already said " Sides opposite to any corner are called the same, only with a small letter." And then draw a triangle in your mind, and apply to the question asked.
could be taken instead A V, but then the included angle will not be WITH A A well, the height will be hb. The result if you check will be the same.
For example, like this (xa,ya) =3.4 (xb,yb) =-6.14 (xc,yc)=-6,-3
writing a request treug xa=3;ya=4;xb=-6;yb=14;xc=-6;yc=-3
and we get
Triangle parameters by given parameters
Side a = 17
Side b = 11.401754250991
Side c = 13.453624047073
Semiperimeter p = 20.927689149032
Angle A = 1.4990243938603 in degrees 85.887771155351
Angle B = 0.73281510178655 in degrees 41.987212495819
Angle C = 0.90975315794426 in degrees 52.125016348905
Triangle area S = 76.5
Height ha per side a = 9
Height hb per side b = 13.418987695398
Height hc per side c = 11.372400437582
Median ma per side a = 9.1241437954466
Median mb per side b = 14.230249470757
Median mc per side c = 12.816005617976
Good luck with your calculations!!
