Suppose is a triangle with sides of lengths , , and that are opposite their respective vertices , , and . Let , , and be the angles at , , and . The Law of Cosines says that
When the appropriate information is known, the Law of Cosines can be used to solve triangles.
Heron's formula for the area of can be derived from the Law of Cosines:
Area , where is the semi-perimeter of the triangle with sides of lengths , , and .