# Solving Oblique Triangles

### The Law of Sines

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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