In order to solve problems which require the application of the Law of Sines, it is necessary to
A typical problem requiring the Law of Sines in order to solve it involves a triangle
in which there is no right angle. We are given some information about a triangle, but we have to find measurements of other sides and/or angles. The Law of Sines for a triangle
ABC is stated below, assuming that the side
opposite angle A
, the side
opposite angle B
, and the side
opposite angle C
Suppose in triangle
are given. Find the measure of side c
. This would be a typical example of this type of problem.
First, we make a diagram. A diagram of this triangle
is shown below.
In this diagram the given distances and angles are labeled:
The variable c
is chosen to represent the unknown measurement of the side
C. This is the object of the question.
To relate the known measurements and the variable, an equation
is written. In this case the equation
involves the ratios of the sines of angles to the opposite sides. We have
We now need to know the measure of angle
B to solve the problem.
The sum of angles A and C is 28º + 91º = 119º. Since the sum of the angles in a triangle
equals 180º we know that angle
B must have a measure of