# Law of cosines

From Citizendium, the Citizens' Compendium

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

where , , and are the lengths of the sides of the triangle opposite to angles , , and , respectively (see Figure 1).