hy·​pot·​e·​nuse | \ hī-ˈpä-tə-ˌnüs How to pronounce hypotenuse (audio) , -ˌnyüz \
variants: or less commonly hypothenuse \ hī-​ˈpä-​thə-​ˌnüs How to pronounce hypothenuse (audio) , -​ˌnyüz \

Definition of hypotenuse

1 : the side of a right-angled triangle that is opposite the right angle
2 : the length of a hypotenuse

Illustration of hypotenuse

Illustration of hypotenuse

ac hypotenuse

Examples of hypotenuse in a Sentence

Recent Examples on the Web The triangle has a base 4 units long, a vertical side 3 units long and a hypotenuse 5 units long going from upper left to lower right. Quanta Magazine, "Solution: ‘Natural Law and Elegant Math’," 17 Jan. 2020 The man addressed me over the cliff of his shoulder—talked down to me in the same condescending way Mister Hughes explained polynomials and hypotenuses. Douglas Stuart, The New Yorker, "Found Wanting," 6 Jan. 2020 The triangle has a base 4 units long, a vertical side 3 units long and a hypotenuse 5 units long going from upper left to lower right. Quanta Magazine, "Does Natural Law Need Elegant Mathematics?," 5 Dec. 2019 If the two legs of a right triangle each have the same rational length, Hippasus is said to have shown, its hypotenuse cannot have a rational length. Quanta Magazine, "Mathematicians Shed Light on Minimalist Conjecture," 9 July 2013 His theorem, a part of Euclidean geometry taught in many high school math classes, states that the hypotenuse of a right triangle (the side opposite the right angle) equals the sum of the squares of the other two sides. Kevin Kelleher, Fortune, "Stonehenge Builders Used Pythagoras' Theorem Centuries Before His Birth, Say Experts," 21 June 2018 Plus it’s gorgeous, the liquid resting on the hypotenuse of a triangular block of ice that’s been frozen into the glass. Esther Mobley, SFChronicle.com, "SF’s Interval puts the fern bar on a cocktail menu," 20 June 2018 Those aren’t scientific concepts with formulas, like gravity or the length of a hypotenuse. Derek Thompson, The Atlantic, "Is Bitcoin the Most Obvious Bubble Ever?," 9 Dec. 2017 This car only looks like a fastback from 270 degrees, thanks to the twin hypotenuse of roof pillars. Dan Neil, WSJ, "Mazda’s MX-5 Miata RF: A Peter-Pan Car Grows Up," 12 Oct. 2017

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'hypotenuse.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of hypotenuse

1594, in the meaning defined at sense 1

History and Etymology for hypotenuse

earlier hypothenusa, hypothenuse, borrowed from Latin hypotēnūsa, borrowed from Greek hypoteínousa, noun derivative (with grammḗ "line" or pleurá "side" understood) from feminine of hypoteínōn, present participle of hypoteínein "to stretch under, put under, subtend," from hypo- hypo- + teínein "to stretch, extend" — more at tenant entry 1

Note: The nominal use of hypoteínousa in Greek is apparent in passages such as the following, from the Deipnosophistae of Athenaeus of Naucratis (10.13), where "line/lines" or "side/sides" are understood: "Apollódōros dè ho arithmētikòs kaì thûsaí phēsin autòn hekatómbēn epì tôi eurēkenai hóti trigṓnou orthogōníou [he] tḕn orthḕn gōnían hypoteínousa íson dýnatai taîs periechoúsais…." ("And Apollodorus the Calculator says that he [Pythagoras] even sacrificed a hecatomb when he discovered that in a right-angled triangle the [square of the] line subtending ("hypoteínousa") the right angle is equal to [the square of] the lines embracing it.)"

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Time Traveler for hypotenuse

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The first known use of hypotenuse was in 1594

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Last Updated

27 Jan 2020

Cite this Entry

“Hypotenuse.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/hypotenuse. Accessed 24 Feb. 2020.

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How to pronounce hypotenuse (audio)

English Language Learners Definition of hypotenuse

mathematics : the long side opposite the right angle of a triangle


hy·​pot·​e·​nuse | \ hī-ˈpä-tə-ˌnüs How to pronounce hypotenuse (audio) , -ˌnyüz \

Kids Definition of hypotenuse

: the side of a right triangle that is opposite the right angle

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Spanish Central: Translation of hypotenuse

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