The hypotenuse is the longest side of a right triangle, opposite the right angle.
The hypotenuse is fundamental to the Pythagorean theorem. It is always the side across from the 90° angle. Its length can be found using c = √(a² + b²) where a and b are the other two sides. The hypotenuse is critical in trigonometry, where the sine, cosine, and tangent ratios are defined using it. The word comes from Greek meaning "stretching under," describing its position opposite the right angle.
The relationship of the hypotenuse to the other sides was known to ancient Babylonians (1800 BCE) and Indians (800 BCE). The Pythagorean theorem, named after Greek mathematician Pythagoras (570-495 BCE), formally proved the relationship. The term "hypotenuse" was used by Plato and Euclid.