**Law of Cosines**

Given SAS or SSS

**13.13** State the law of cosines, given a triangle *ABC* such that *a* is the length of the side opposite angle *A*, *b* is the length of the side opposite angle *B*, and *c* is the length of the side opposite angle *C*.

The law of cosines takes one of three forms, based on the information you are given in the problem. In each case, the square of the length of one side is equal to the sum of the squares of the other side lengths minus double the product of those lengths multiplied by the cosine of the angle opposite the original side.

Added bonus: There is no ambiguous case for the law of cosines. If the formula produces an answer, you can be sure that answer is correct.

*Problems 13.14–13.17 refer to triangle ABC, illustrated ...*

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