Hypotenuse

In geometry, a hypotenuse is the side of a right triangle opposite the right angle. It is the longest side of any such triangle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. Mathematically, this can be written as ${\displaystyle a^{2}+b^{2}=c^{2}}$, where a is the length of one leg, b is the length of another leg, and c is the length of the hypotenuse.

For example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse is the square root of 25, that is, 5. In other words, if ${\displaystyle a=3}$ and ${\displaystyle b=4}$, then ${\displaystyle c={\sqrt {a^{2}+b^{2}}}=5}$.