Hypotenuse

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In geometry, a hypotenuse is the side of a right triangle opposite the right angle.^[1] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. 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 two legs. 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.^[2]

For example, if one of the legs of a right angle has a length of 3 and the other has a length of 4, then their squares add up to 25 = 9 + 16 = 3 × 3 + 4 × 4. Since 25 is the square of the hypotenuse, 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 ${\displaystyle c={\sqrt {a^{2}+b^{2}}}=5}$.