The cosine rule

We can use the cosine formula to find the length of a side or size of an angle.

For a triangle with sides a,b and c and angles A, B and C 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

These formulas can be rearranged to give :

When to use it

We can use the cosine formula when we are given:

• Two sides and an angle.

  

• Three sides.

  

Check whether your formula sheet gives these formulas in both formats. If it does not, you may need to rearrange them yourself.