Hypotenuse

Pronunciation: /haɪˈpɒ.tnˌus/ Explain

Click on the blue points and drag them to change the figure. 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:

Click on the blue points and drag them to change the figure. 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:

References

1. McAdams, David E.. All Math Words Dictionary, hypotenuse. 2nd Classroom edition 20150108-4799968. pg 93. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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
3. Robert Louis Short , William Harris Elson. Secondary-school Mathematics. pp 54-55. 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. https://www.allmathwords.org/en/r/righttriangle.html.

Educator Resources

• Pythagoras Theorem and Ellipses. NASA Connect. 2/18/2010. http://www.archive.org/details/NasaConnect-Goe-PythagorasTheoremAndEllipses/index.htm.

Cite this article as:

McAdams, David E. Hypotenuse. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/h/hypotenuse.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.)