Law of Cosines
Pronunciation: /lɔ ʌv ˈkoʊ.saɪnz/ Explain
The law of cosines relates the
angles
of a
triangle
to the length of the sides:
c^{2} =
a^{2} + b^{2} 
2ab cosγ.. The
law of cosines is a
generalization
of the pythagorean theorem.
Since cos(90°) is zero, the formula is
c^{2} =
a^{2} + b^{2}
for right triangles.
A geometric equivalent of the law of cosines was described in
Euclid's
Elements,
Book 2,
proposition 12
and
proposition 13.
The law of cosines can also be used to generate the formula for the angle
opposite side c, if one knows the lengths of the sides:

Click on the blue points on the figure and drag them to change the figure.
 Manipulative 1  Law of Cosines Created with GeoGebra. 

References
 McAdams, David E.. All Math Words Dictionary, law of cosines. 2nd Classroom edition 201501084799968. pg 106. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
 McAdams, David E.. Triangle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 8/31/2018. http://www.allmathwords.org/en/t/triangle.html.
 Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.
Cite this article as:
McAdams, David E. Law of Cosines. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/l/lawofcosines.html.
Image Credits
Revision History
4/23/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
8/31/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
7/18/2018: Initial version. (
McAdams, David E.)