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).