hypotenuse

American  

[hahy-pot-n-oos, -yoos] / haɪˈpɒt nˌus, -ˌyus /

noun

Geometry.

1. the side of a right triangle opposite the right angle.

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hypotenuse British  

/ haɪˈpɒtɪˌnjuːz /

noun

1.  hyp.  the side in a right-angled triangle that is opposite the right angle

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hypotenuse Scientific  

/ hī-pŏt′n-o̅o̅s′ /

1. The side of a right triangle opposite the right angle. It is the longest side, and the square of its length is equal to the sum of the squares of the lengths of the other two sides.

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hypotenuse Cultural  

1. In a right triangle (a triangle that has one right angle), the side opposite the right angle. (See Pythagorean theorem.)

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Etymology

Origin of hypotenuse

1565–75; earlier hypotenusa < Latin hypotēnūsa < Greek hypoteínousa ( grámmē ) subtending (line) (feminine present participle of hypoteínein to subtend), equivalent to hypo- hypo- + tein- stretch ( see thin) + -ousa feminine present participle suffix

Explanation

The hypotenuse is the side of a right triangle that’s opposite the 90-degree angle. It’s a term specific to math, specifically geometry. Hypotenuse comes from the Greek word hypoteinousa which means "stretching under." The hypotenuse “stretches under” the right angle of a triangle, which has an angle of 90 degrees. A right angle is the kind of angle that appears four times in squares and rectangles. If your triangle has a right angle, the line opposite that angle is the hypotenuse.

Example Sentences

The hypotenuse of that triangle then has the length √2.

From Scientific American • May 23, 2023

So could you talk about the hypotenuse of a triangle?

From Salon • May 21, 2023

Its strangeness lay in how Leonardo’s sketch showed an adjoining pitcher and, pouring from its spout, a series of circles that formed the triangle’s hypotenuse.

From New York Times • Feb. 17, 2023

The triangle, it must be said, is beautifully balanced, but Groff for me is the emotional hypotenuse of a production that I can’t wait to see again after it moves to Broadway in the fall.

From Los Angeles Times • Jan. 5, 2023

In the Meno Socrates persuaded an uneducated slave boy that he already knew that the square on the hypotenuse is equal to the sum of the squares of the other two sides.

From "The Invention of Science" by David Wootton