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.^{[2]}
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:

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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:
a^{2} + b^{2} = c^{2} 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:

References
 McAdams, David E.. All Math Words Dictionary, hypotenuse. 2nd Classroom edition 201501084799968. pg 93. Life is a Story Problem LLC. January 8, 2015. Buy the book
 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 7/18/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/16/mode/1up. Buy the book
 Robert Louis Short , William Harris Elson. Secondaryschool Mathematics. pp 5455. www.archive.org. D. C. Heath & Co.. 1910. Last Accessed 7/18/2018. 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. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/hypotenuse.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)