The Cosine Law

To this point we have examined the right-angled trigonometric ratios to help us solve problems involving right-angled triangles. We have also looked at the sine law to help us solve certain non-right triangle problems. But what happens when we are given a non-right triangle that cannot be solved using the sine law, like the triangle below?

Notice that we are NOT given an angle AND a side opposite that angle. Therefore, we cannot use the sine law. To illustrate this fact, fill the given information into the sine law:

Notice that we are not given a 'complete ratio'. (None of the fractions have a value in both the numerator and the denominator). We cannot use the sine law. Therefore, we need a new tool: the cosine law.

What would you like to do?

• See the cosine law and some examples of how it works.
• Try some sample cosine law questions.