What is the cosine rule and when can it be used?

The cosine rule is used to find the length of a side or size of an angle. 

Take a look at the triangle below: 

 

For this triangle we have sides a, b and c and angles A,B and C. 

 

For this triangle the cosine rule can be written as: 

 

a² = b² + c²- 2bc Cos A

OR

b² = a² + c²- 2ac Cos B

OR 

c² = a² + b²- 2ab Cos C

 

You use the above formula to work out a missing side of the triangle.

 

If you want to work out a missing angle, we rearrange the formula above to these:

 

 

 

 

And we can use these formula to work out angles in the triangle. 

 

When to use the cosine rule:

Remember we can only use the cosine rule in 2 situations: 

 

1) If we already know 2 sides and 1 angle (shown below) 

2) If we already know 3 sides (shown below)