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:
![image0.png](https://www.dummies.com/wp-content/uploads/277341.image0.png)
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.
![image1.jpg](https://www.dummies.com/wp-content/uploads/277342.image1.jpg)
The preceding figure shows how the Pythagorean Theorem works for a right triangle with legs of 3 and 4 and a hypotenuse of 5.