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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
b2 = a2 + c2- 2ac Cos B
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)