The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle. This same relationship is often used in the construction industry and is referred to as the 3-4-5 Rule.

The right triangle below has one leg with a length of three, another leg with a length of four and a hypotenuse with a length of five.

Given the lengths of any two sides of a right triangle, the length of the third side can be calculated using the Pythagorean theorem. In the example above, there are three possible unknowns. Each case is outlined below.

There are many ways to prove the Pythagorean theorem. One such proof is given here.