In order to solve problems which require the application of the Law of Cosines, it is necessary to

A typical problem that requires the use of the Law of Cosines 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 Cosines 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**:

This can also be written as

First, we make a diagram. A diagram of this

triangle is shown below.

In the diagram, known angles and lengths of sides are labeled:

The

variable **a** is chosen to represent the unknown measurement of the

side opposite

angle A. 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 Law of Cosines, keeping

side **a** on the opposite

side of the

equation from

angle A.

We have

which is the same as

We finish solving for a by taking the

square root of 12.197 and we get