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

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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)

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