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.


Figure 1: Right triangles 


Figure 2: Object that are not right triangles 

Parts of a Right Triangle
 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:
 Definition of sine:
 Definition of cosine:
 Definition of tangent:
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.

Manipulative 2: Solving a Right Triangle. Created with GeoGebra. 
References
 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: 20100102). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/8/mode/1up/search/right.
More Information
 Joyce, D.. Right Triangles. clark.edu. 20091128. http://www.clarku.edu/~djoyce/trig/right.html.
 Special Right Triangles. onlinemathlearning.com. 20091128. http://www.onlinemathlearning.com/specialrighttriangles.html.
Educator Resources
 Pythagoras Theorem and Ellipses. NASA Connect. NASA LaRC Office of Education. 20100218. http://www.archive.org/details/NasaConnectGoePythagorasTheoremAndEllipses.
Printed Resources
Cite this article as:
Right Triangle. 20091128. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/righttriangle.html.
Translations
Image Credits
Revision History
20091221: Added "References" (
McAdams, David.)
20091128: Rewrote article. (
McAdams, David.)
20070711: Initial version (
McAdams, David.)