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** is

**a**, the

side opposite

**angle B** is

**b**, and the

side opposite

**angle C** is

**c**:

Suppose in

triangle ABC that

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 opposite

angle 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

.

.

.