# Applying the Pythagorean Theorem

The Pythagorean Theorem has been known for at least 2,500 years. You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the third side.

**The Pythagorean Theorem:** The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse:

Here, *a* and *b* are the lengths of the legs and *c* is the length of the hypotenuse. The legs are the two short sides that touch the right angle, and the *hypotenuse* (the longest side) is opposite the right angle.

The preceding figure shows how the Pythagorean Theorem works for a right triangle with legs of 3 and 4 and a hypotenuse of 5.