The Pythagorean theorem

The relationship that holds every right triangle together.

The idea

For a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. The hypotenuse, c, is always opposite the 90° angle and is the longest side.

Work through an example

With legs of 6 and 8, c² = 6² + 8² = 36 + 64 = 100, so c = 10. To find a missing leg instead, rearrange: a = √(c² − b²).

What to watch for

This relationship only applies directly to right triangles. For an arbitrary triangle, use the law of cosines.