Hypotenuse

Pronunciation: /haɪˈpɒ tnˌus/ ?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 1: Hypotenuse. Manipulative 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

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 2: Length of the hypotenuse of a right triangle 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. hypotenuse. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=hypotenuse&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pg 16. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-28). http://www.archive.org/stream/elementsofconstr00noetrich#page/16/mode/1up.
  3. Robert Louis Short , William Harris Elson. Secondary-school Mathematics, pp 54-55. D. C. Heath & Co., 1910. (Accessed: 2010-02-10). http://www.archive.org/stream/secondaryschool00elsogoog#page/n68/mode/1up.

More Information

  • McAdams, David. Right Triangle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Right%20Triangle.
  • McAdams, David. Angle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Angle.

Educator Resources

  • Pythagoras Theorem and Ellipses. NASA Connect. NASA LaRC Office of Education. 2010-02-18. http://www.archive.org/details/NasaConnect-Goe-PythagorasTheoremAndEllipses.

Printed Resources

Cite this article as:


Hypotenuse. 2010-02-10. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/hypotenuse.html.

Translations

Image Credits

Revision History


2010-02-10: Added "References" (McAdams, David.)
2009-05-06: Added usage of hypotenuse in right angle trigonometry. (McAdams, David.)
2008-09-15: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License