What does hypotenuse mean?
A hypotenuse is the side of a right-angled triangle that lies opposite the right angle. It is necessarily the triangle's longest side, whereas the other two sides, called the legs, meet at the right angle. The word is most closely associated with the Pythagorean theorem, which states that the square of the hypotenuse equals the sum of the squares of the two legs. In everyday geometry, a hypotenuse can be calculated from the lengths of the other two sides using square roots, and its length can also be used to determine the lengths of the shorter sides. The term is specialized rather than poetic or figurative, so it normally appears in mathematical, architectural, surveying, or technical contexts.
nounIn a right-angled triangle, the hypotenuse is the side opposite the right angle. It is also the longest side of the triangle.
- The side of a right-angled triangle that is opposite the right angle and is longer than either of the other two sides.
"The Pythagorean theorem can be used to calculate the hypotenuse when the lengths of the two shorter sides are known."
"The hypotenuse measures 13 units when the two shorter sides measure 5 and 12 units."
"The triangle's hypotenuse forms the diagonal of the rectangular base."
The regular plural is hypotenuses.
"The two hypotenuses of the adjoining triangles share a common vertex."
The hypotenuse is the longest side of a right triangle, but it is not one of the two perpendicular legs that meet at the right angle.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does hypotenuse come from?
The word comes from Greek hypotenous, meaning “stretching under,” and specifically refers to the side stretched opposite or beneath the right angle in a right triangle. It was borrowed into Latin and then into English, where it became the standard geometric term for this longest side.
Related word forms
How hypotenuse is actually used
The term is specific to geometry and is normally used only for a right-angled triangle.