The Law of Cosines

The law of cosines is useful in calculating the length of an unknown side of an oblique triangle when the length of the other two sides and the size of their included angle is known.

The law of cosines is sometimes called the generalized Pythagorean theorem .

Consider the acute oblique triangle shown in Figure 21.14 A and the obtuse oblique triangle shown in Figure 21.14 B . In both triangles, the following relationships are true: