Right Triangle

Pronunciation: /raɪt ˈtraɪˌæŋ gəl/ ?

A right triangle is a triangle with one right angle[1]. A right angle is an angle at the intersection of two perpendicular lines. The measure of a right angle is 90 °, which is the same as π/2 rad.

Examples
These triangles are right triangles. These shapes are not right triangles. Either they are not triangles, or they do not have one right angle.
right triangles having one right angle.
Figure 1: Right triangles
Shapes that are not right triangles.
Figure 2: Object that are not right triangles

Parts of a Right Triangle

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: Parts of a Right Triangle. Created with GeoGebra.

Some parts of a right triangle are named more specifically than the names for the same parts of a general triangle. The boundaries of a general triangle are called sides. The sides opposite the right angle of a right triangle is called an hypotenuse, and the other two sides are called the legs of the right triangle.

Solving Right Triangles

To solve a right triangle is to find an unknown value related to the right triangle from known values. There are a number of identities that can be used to solve right triangles:

  • Pythagorean theorem: a^2+b^2=c^2
  • Definition of sine: sin(A) = a/c, sin(B) = b/c
  • Definition of cosine: cos(A) = b/c, cos(B) = a/c
  • Definition of tangent: tan(A) = a/b, tan(B) = b/a

To solve a right triangle, find an identity in the list above that has all knowns except for one unknown, fill in the know values, then solve for the unknown. In more complicated problems, two equations and two unknowns can be used. Click on the blue dots in manipulative 2 and drag them to change the figure. Click on the 'Show Pythagorean theorem' check box to see an example of solving a right triangle using the Pythagorean theorem. Click on the 'Show trigonometric function' checkbox to see and example of solving a right triangle using a trigonometric function.

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: Solving a Right Triangle. Created with GeoGebra.

References

  1. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 8. Translated by Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/right.

More Information

  • Joyce, D.. Right Triangles. clark.edu. 2009-11-28. http://www.clarku.edu/~djoyce/trig/right.html.
  • Special Right Triangles. onlinemathlearning.com. 2009-11-28. http://www.onlinemathlearning.com/special-right-triangles.html.

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:


Right Triangle. 2009-11-28. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/righttriangle.html.

Translations

Image Credits

Revision History


2009-12-21: Added "References" (McAdams, David.)
2009-11-28: Rewrote article. (McAdams, David.)
2007-07-11: 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