Hypotenuse Calculator - Pythagorean math geometry

A right triangle (one where one interior angle is 90°), the longest side is called the hypotenuse. It is always the side opposite the 90° angle. See Right Triangle definition.

Pythagoras' Theorem applies to right triangles and states (in word form):

"The square on the hypotenuse is equal to the sum of the squares on the other two sides."

WHAT IS HYPOTENUSE THEOREM?

The Pythagorean theorem describes how the three sides of a right triangle are related in Euclidean geometry. It states that the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. You can also think of this theorem as the hypotenuse formula. If the sides of a right triangle are x and y and the hypotenuse is z, the formula is

x² + y² = z²

The theorem was credited to the ancient Greek philosopher and mathematician Pythagoras, who lived in the sixth century BC. Although it was previously used by the Indians and Babylonians, Pythagoras (or his students) were credited to be the first to prove the theorem. It should be noted that there is no concrete evidence that Pythagoras himself worked on or proved this theorem.



WHAT IS HYPOTENUSE FORMULA?

The hypotenuse formula is simply taking the Pythagorean theorem and solving for the hypotenuse, z. Solving for the hypotenuse, we simply take the square root of both sides of the equation x² + y² = z²and solve for z. When doing so, we get z = √(x² + y²). This is just an extension of the Pythagorean theorem and often is not associated with the name hypotenuse formula.