Law of cosines
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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.
Let be oriented so that is at the origin, and is at the point.
is the distance from to .
Substituting the appropriate points into the distance formula gives us
Squaring the inner terms, we have
Square both sides for
Complete the triangle using the law of cosines.
To find the side length ,