Hypotenuse

Pronunciation: /haɪˈpɒ tnˌus/ Explain

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Manipulative 1 - Hypotenuse Created with GeoGebra.

The hypotenuse of a right triangle is the side opposite the right angle.[1] Click on the blue points in the manipulative and drag them to change the figure.

The length of the hypotenuse of a right triangle is used to help define the sine and cosine functions:

sine = opposite/hypotenuse, cosine = adjacent/hypotenuse

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Manipulative 2 - Hypotenuse Created with GeoGebra.

The length of an hypotenuse of a right triangle can be calculated from the length of the legs of a right triangle using the Pythagorean theorem: a2 + b2 = c2 where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse. For example, if the length of the legs are 3 and 4, the length of the hypotenuse is:

c^2=a^2+b62,a=3,b=4 implies c^2=3^2+4^2 implies c^2=9+16 implies c^2=25 implies c=square root of 25 implies c=5

References

  1. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 16. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 8/6/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/16/mode/1up. Buy the book
  2. Robert Louis Short , William Harris Elson. Secondary-school Mathematics. pp 54-55. www.archive.org. D. C. Heath & Co.. 1910. Last Accessed 8/6/2018. http://www.archive.org/stream/secondaryschool00elsogoog#page/n68/mode/1up. Buy the book

More Information

  • McAdams, David E.. Right Triangle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/r/righttriangle.html.

Educator Resources

Cite this article as:

McAdams, David E. Hypotenuse. 7/18/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/hypotenuse.html.

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Revision History

7/16/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/10/2010: Added "References". (McAdams, David E.)
5/6/2009: Added usage of hypotenuse in right angle trigonometry. (McAdams, David E.)
9/15/2008: Initial version. (McAdams, David E.)

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