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.
