Editing Hypotenuse (section)

{{short description|Longest side of a right-angled triangle, the side opposite of the right angle}}
{{technical|date=May 2019}}
[[File:Hypotenuse.svg|thumb|right|A right-angled triangle and its hypotenuse]]
In [[geometry]], a '''hypotenuse''' is the side of a [[right triangle]] opposite the [[right angle]].<ref>{{Cite EB1911 |wstitle= Triangle (geometry) |volume= 27 |page= 258|quote=...Also a right-angled triangle has one angle a right angle, the side opposite this angle being called the hypotenuse;...|short=1}}</ref> 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 (algebra)|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 <math>a^2 + b^2 = c^2</math>, where ''a'' is the length of one leg, ''b'' is the length of another leg, and ''c'' is the length of the hypotenuse.<ref>{{Cite book |last=Jr |first=Jesse Moland |url=https://books.google.com/books?id=dWAXwWpQa5EC&q=hypotenuse |title=I Hate Trig!: A Practical Guide to Understanding Trigonometry |date=August 2009 |publisher=Jesse Moland |isbn=978-1-4486-4707-1 |pages=1 |language=en}}</ref>

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 &times; 3 + 4 &times; 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 <math>a = 3</math> and <math>b = 4</math>, then <math>c = \sqrt{a^2 + b^2} = 5</math>.