# How to find the leg?

The legs are two sides of the triangle, forming a right angle, i.e. there are legs only in a right triangle. And now we will talk about how to find the side of the triangle.

## How to find a leg: designations and formulas

### Legend

- let the first leg is "k", the second one is "m", these are the sides that form the angle 900(right angle);
- hypotenuse length - "s";
- angle A - opposite the leg "k";
- angle B - opposite the leg "m".

### Ways of finding the leg

#### Pythagorean theorem

With the help of the Pythagorean theorem, one can find the leg of a right triangle when the length of the hypotenuse and the length of one of the legs are known.

According to the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the length of the hypotenuse.

A hypotenuse is a side of a triangle that lies opposite a right angle (that is, it exists only in a right-angled triangle).

s2= k2+ m2; from here we find the leg "k":

k2= s2-m2or k = square root of (s2-m2)

#### Trigonometric functions

They will help in finding the leg, if one of the acute angles and the length of the hypotenuse is known (variant 1).Or if one of the acute angles and the length of one of the legs is known (option 2).

Method 1.

When the length of the hypotenuse "s" and one acute angle are known, for example, angle A. Then:

- k = s * sin (A)

That is: the length of the leg is the product of the cosine of the adjacent angle and the length of the hypotenuse. - m = s * cos (A)

That is: the length of the leg is the product of the sine of the adjacent angle and the length of the hypotenuse.

Method 2

When the length of one of the legs is known, for example, "k" and one acute angle, for example, A. Then:

- m = k * tg (A)

And vice versa: if the leg b and the acute angle B are known, then: - k = m * tg (B)

That is: the length of the leg is the product of the length of the second leg and the tangent of the angle lying against the desired leg.

This method also allows you to find the hypotenuse: s = k * sin (A)

We looked at the basic ways that will tell you how to find the leg of a right triangle; led the necessary formulas.