Right Triangle

Pronunciation: /raɪt ˈtraɪˌæŋ.gəl/ Explain

A right triangle is a triangle with one right angle[2]. A right angle is an angle formed by 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

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

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 side 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 'Solve using the Pythagorean theorem' check box in manipulative 2 to see an example of solving a right triangle using the Pythagorean theorem. Click on the 'Solve using a trigonometric function' checkbox to see and example of solving a right triangle using a trigonometric function.

Click on the blue points and drag them to change the figure. Click on the check box for an example of solving a right triangle.

Manipulative 2 - Solving a Right Triangle Created with GeoGebra.

References

  1. McAdams, David E.. All Math Words Dictionary, right triangle. 2nd Classroom edition 20150108-4799968. pg 157. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. 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.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 12/4/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/right. Buy the book

More Information

  • Joyce, D.. Right Triangles. clark.edu. 11/28/2009. http://www.clarku.edu/~djoyce/trig/right.html.

Educator Resources

Cite this article as:

 McAdams, David E. Right Triangle. 5/2/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/righttriangle.html.

Image Credits

Revision History

5/2/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/16/2018: Fixed table formatting problem. (McAdams, David E.)
12/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/21/2009: Added "References". (McAdams, David E.)
11/28/2009: Rewrote article. (McAdams, David E.)
7/11/2007: Initial version. (McAdams, David E.)

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