What is the Pythagorean theorem and how do you use it?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides:

a² + b² = c²

Where c is the hypotenuse and a, b are the legs.

Example: Find the hypotenuse when a = 3 and b = 4:
3² + 4² = c²
9 + 16 = c²
25 = c²
c = 5

You can also use it to find a missing leg: if c = 13 and a = 5, then b² = 13² − 5² = 169 − 25 = 144, so b = 12.