What is the "law of tangents"?

The law of tangents states that for a triangle with sides a, b and c and corresponding angles A, B and C, (a - b)/(a + b) is equal to the tangent of (1/2[A - B])/(1/2[A + B]).

The law of tangents can be used when the length of two sides and the size of the angle in between them are known, such as the values for b, c and A. The law can also be used when the values of any two angles and one side are known, such as A, B and a. The law of tangents is a trigonometric function.