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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