The Law of Sines states that each side of a triangle is proportional to the sine of the opposite angle. It looks like this:

The law of sines can be used when two angles and a side of a triangle are known.

Consider the following problem, in which we have two angles and the side opposite one of them: A = 35^o, B = 49^o, and a = 7. The first part we calculate is the third angle, C. C = 180^o -35^o -49^o = 96^o. Then, using the Law of Sines, b and c can be calculated. = = = = = . b 9.21, and c 12.13.

Now we'll consider two angles and the side included: A = 27^o, B = 105^o, and c = 13. First we'll calculate the measure of the third angle, C. C = 180^o -27^o -105^o = 48^o. Then using the Law of Sines, a and b can be calculated, much like we did in the previous example.