# How to find a leg if the corner is known

When the leg is mentioned in statements of the problem, it means that in additions to all parameters specified in them also one of triangle corners is known. This useful circumstance in calculations is caused by the fact that such term call only the party of a rectangular triangle. Moreover, if the party is called a leg, means to you it is known that it is not the longest in this triangle and adjoins a corner in 90 °.

## Instruction

1. If the only known corner is equal 90 °, and lengths of two parties of a triangle are specified in conditions (b and c), define which of them is a hypotenuse - it has to be the party of the big sizes. Then use Pythagorean theorem and calculate length of an unknown leg (a) extraction of a square root from the difference of squares of lengths of the bigger and smaller parties: a = √ (with²-b²). However, it is possible not to find out which of the parties is a hypotenuse, and for extraction of a root to use the module of a difference of squares of their lengths.

2. Knowing length of a hypotenuse (c) and size of the corner (α) lying opposite the necessary leg (a) use in calculations definition of trigonometrical function a sine through acute angles of a rectangular triangle. It definition claims that the sine of the corner, known from conditions, is equal to a ratio between lengths of an opposite leg and hypotenuse, so, for calculation of required size multiply this sine by hypotenuse length: = sin (α)*s.

3. If except hypotenuse length (c) corner size (β), adjacent to a required leg (a) is given, use definition of other funkiya - a cosine. It sounds likewise, so, before calculation just replace designations of function and a corner in a formula from the previous step: = cos (β)*s.

4. Function a cotangent will help with calculation of length of a leg (a) if in the conditions of the previous step the hypotenuse is replaced with the second leg (b). By definition the size of this trigonometrical function is equal to a ratio of lengths of legs therefore increase a cotangent of the known corner by length of the known party: = ctg (β)*b.

5. Use a tangent for calculation of length of a leg (a) if in conditions there are a corner size (α) lying in opposite top of a triangle and length of the second leg (b). According to definition the tangent of the corner, known from conditions, is the relation of length of the required party to length of the known leg therefore multiply the size of this trigonometrical function from the set corner at length of the known party: = tg (α)*b.

Author: «MirrorInfo» Dream Team