# Pythagorean Theorem

## Table of Contents

For any right triangle *abc* (see diagram below):

The lengths of the sides are related by the Pythagorean Theorem:

$$a^2 + b^2 = c^2$$

Where

- \(a\) and \(b\) are the lengths of the legs of the triangle, and
- \(c\) is the length of the hypotenuse

## Sources: #

## Example #

After being rejected by a girl, Kevin bends forward to pick up his hurt ego. His legs contact the floor at a right angle and his arms + torso miraculously reach the ground in front of him.

If his legs are 30 meters long, and his arms + torso are 50 meters long, how far away is his ego from his legs?

Using the diagram above, a = 30m and c = 50m. Using the pythagorean theorem:

$$ a^2 + b^2 = c^2 \Longrightarrow b = \sqrt{c^2 - a^2} = \sqrt{1600} = 40m$$