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.

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