The Pythagorean Theorem is a simple mathematical equation with various uses today in geometry, trigonometry, architecture, and more.  The equation is as follows:

a² + b² = c²

This only applies for a right triangle, that is, a triangle that has a 90 degree angle.  C is the hypotenuse (the longest side), and A and B are the two other sides.  Thus if you know A and B, you can easily calculate C by using square roots.  Likewise if you know B and C or A and C.

The ability to find out this length quickly is useful in trigonometric and geometric proofs, as well as lengths for physics, and designs in architecture.