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


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:


cos A = b to the power 2 + c to the power 2 - a to the power 2 over 2 b c


cos B = a to the power 2 + c to the power 2 - b to the power 2 divided by 2 a c


cos C = a to the power 2 + b to the power 2 - c to the power 2


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) 

image: triangle

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


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