# Law of cosines

Figure 1: A generic triangle with sides of length a, b, and c opposite the angles A, B, and C.

In geometry the law of cosines is a useful identity for determining an angle or the length of one side of a triangle when given either two angles and three lengths or three angles and two lengths. When dealing with a right triangle, the law of cosines reduces to the Pythagorean theorem because of the fact that cos(90°)=0. To determine the areas of triangles, see the law of sines. The law of cosines can be stated as

$c^2 = \left(a^2 + b^2\right) - 2ab\cos(C)$

where a, b, and c are the lengths of the sides of the triangle opposite to angles A, B, and C, respectively (see Figure 1).