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.