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title: Law of Cosines
---
## Law of Cosines

The Law of Cosines can be used to find the ramaining sides or angles of a non-right triangle when given either the length of two sides and its included angle (SAS) or the lengths of the three sides (SSS).
The Law of Cosines states:
<img src="http://hyperphysics.phy-astr.gsu.edu/hbase/imgmth/lcos.gif">

This looks very similar to the Pythagorean Theorem, and if C was 90 degrees (a right triange), the expression acctually simplifies to the Pythagorean Thoerem.  So, the Pythagorean Theorem is a special case of the Law of Cosines.

You can also switch the angle C with either A or B, but make sure to change the respective side (c) to a or b.

<img src="http://www.mathwarehouse.com/trigonometry/images/law-of-cosines/law-of-cosines-formula-and-picture2.png">

Ex:

<img src="http://www.mathwarehouse.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/images/picture-of-law-of-cosines.png">
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#### More Information:
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https://www.varsitytutors.com/hotmath/hotmath_help/topics/law-of-cosines
http://mathworld.wolfram.com/LawofCosines.html