# Law of cosines

### From Math Images

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<math> c^{2} = (a^{2}+b^{2}-2ab \cos C+b^{2}</math> | <math> c^{2} = (a^{2}+b^{2}-2ab \cos C+b^{2}</math> | ||

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+ | ==example triangulation== |

## Revision as of 09:37, 30 May 2011

The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of a particular angle.

When to use it: SAS, SSS.

## Proof

Let be oriented so that is at the origin, and is at the point.

### Distance Formula

is the distance from to .

Substituting the appropriate points into the distance formula gives us

Squaring the inner terms, we have

Since ,

Square both sides for