Hypotenuse

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (May 2019) (Learn how and when to remove this message) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Hypotenuse" – news · newspapers · books · scholar · JSTOR (May 2019) (Learn how and when to remove this message) (Learn how and when to remove this message)

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 ${\displaystyle c={\sqrt {a^{2}+b^{2}}}=5}$.