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How to find the side of a triangle?

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

At the moment there are several different ways to solve this problem. And each method differs from the previous one not only by the formula by which the calculation is made, but also by the source data that is necessary for the calculation.

Ways of 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 using the formula. Depending on the source data, the formulas can be very different. Usually the required side of the triangle can be calculated by:

  1. Two already known sides and a corner that is between them.
  2. Two corners and one famous side.

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

How to find the unknown side of the triangle

So, to find the side of a triangle which is not known by the condition using the first method, it is necessary to use the following formula: c = v (and2+ b2-2ab * cosC). As for the notation of this formula, 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 an unknown side in a triangle, there is absolutely no need to have any special algebraic knowledge, it is enough to know the basics.

In order to find the side of the second method, we need the following formula: sinA / a = sinB / b = sinC / s. The designations of this formula are similar to the previous one, that is, B and C denote known angles, and C - the only known side.

But in order for the data obtained in the course of calculations to be accurate, it is necessary to make calculations very carefully and correctly, it is best to carry them out twice, and in case of inconsistencies between the results, to make calculations again.

Triangle having the same sides

The standard formula for calculating the search for an unknown side of an ordinary triangle has been given above. But it is always necessary to remember that in order to find the side of an isosceles triangle, they are not suitable. And therefore, to solve this issue, there are special individual formulas that are suitable only for this triangle.

So, first of all, be sure to remember that the height of such a triangle is, at the same time, its median. And the side that needs to be found will be its hypotenuse. As everyone knows, since the school curriculum, the hypotenuse of this triangle is found according to 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 that the calculation of the unknown side of any triangle is a very complicated and time-consuming exercise, this is not quite so. It will be difficult only for the first time.


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