How to find the side of the triangle?

Of course, most often the question of how to findthe unknown side of the triangle arises when carrying out algebraic or geometric calculations, but sometimes such a need arises in ordinary life, for example, when constructing any architectural drawings or carrying out calculations.

At the moment there are severaldifferent ways of solving such a problem. And each method differs from the previous one not only with the formula by which the calculation is made, but also with the initial data that is necessary for calculation.

Methods for finding the sides of a triangle

So, the simplest and most logical answer to the question: how to find the sides of a triangle, is that it is necessary to find a solution by the formula. Depending on the initial data, the formulas can be very different. Usually the required side of the triangle can be calculated by:

  1. The two already known sides and the corner that lies between them.
  2. Two corners and one known side.

As can be seen, in any of the two cases mentioned above,you still need to know the values ​​of the three indicators. Without their knowledge, it will never be possible to find an answer to the question of how to find the sides of a triangle.

How to find the unknown side of a triangle

So, in order to find the side of the triangle which is not known by hypothesis by the first method, it is necessary to use the following formula: c = v (a2+ b2-2аb * cosC). As for the notation of this formula, then a and b are the lengths of the known sides, cosC is the angle between them. In fact, to solve the problem of how to find the unknown side in the triangle, there is absolutely no need to have any special algebraic knowledge, it is enough to know the basics.

In order to find a side by the second methodthe following formula will be needed: sinA / a = sinB / b = sinC / c. The designations of this formula are similar to the previous ones, that is, B and C denote known angles, and C is the only known side.

But in order for the resulting calculationsthe data was accurate, it is necessary to make very careful and correct calculations, it is best to conduct them twice, and in case of inconsistency of the results to each other, to make a calculation again.

Triangle having the same sides

Standard formula for calculating unknown searchesThe sides of the usual triangle were given above. But it must always be remembered that in order to find the side of an isosceles triangle, they do not fit. Therefore, to solve this problem, there are special separate formulas that are suitable only for a given triangle.

So, in the first place, it is necessaryremember that the height of such a triangle is, at the same time, its median. And the side to be found will be its hypotenuse. As everyone knows, since the school program, the hypotenuse of this triangle is based on the Pythagorean theorem. Therefore, in order to find the hypotenuse it is necessary to find the sum of the lengths of the known sides, and extract the root from the result obtained.

And although, at first glance, it may seem thatcalculating the unknown side of any triangle is a very complicated and time-consuming task, it's not quite true. It will be difficult only for the first time. The main thing is to correctly follow the formula for each specific task, and to check the result several times.

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