# Law of cosines

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

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