The cosine law can also be written as

or

These three versions are identical. However, one may be easier to use than another depending on how a given triangle is labelled.

Also notice the relationship between the side represented on the left side of the cosine law and the angle used on the right side. They are opposite one another in a triangle.

Example 2

Determine the value of x.

It often helps to label the triangle using A, B, C, and a, b, and c.

You are working with three sides and one angle, so you can use the cosine law. B is the angle you are given and b is the side you need to find, so it makes sense to use the version of the cosine law.

When using the sine law, you determined both unknown angles as well as unknown sides. The cosine law can also be used to determine unknown angles.

Example 3

Determine the measure of angle y.

Begin by labelling the diagram.

You are working with three sides and one angle, so you can use the cosine law. The angle you are working to find is labelled A so is a good version of the cosine law to use.