Hypotenuse

In geometry, a hypotenuse (alternate spelling: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle. The length of the hypotenuse of a right triangle 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. 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.

Etymology

The word hypotenuse means essentially "length under", and derives from Latin hypotēnūsa, a transliteration of Ancient Greek hypoteínousa (pleurā́ or grammḗ), the feminine present participle of hypoteínō, a combination of hypó ("under") and teínō ("I stretch" or "length"). The word ὑποτείνουσα was used for the hypotenuse of a triangle by Plato in the Timaeus (dialogue) 54d and by many other ancient authors.