The "cosine rule"

Often the triangles occurring in real problems are not right-angled, in which case we can use the "sine rule" and the "cosine rule" to help us.

In the triangle below, the three sides have lengths a, b and c and angles A, B and C. Notice that the side of length a is opposite the angle A, and similarly for b and c.

Here's the cosine rule:

a²=b²+c²- 2bccosA

This allows us to work out any length and angle that we don't know, provided we do know some of the lengths and angles in the triangle.

For example, suppose we know that angle A in the triangle above is 45^o, that length b is 2 units and length c is 3 units.

Can you work out the remaining angles B and C and the length a using the cosine rule?
Here's the answer