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:

 

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) 

 

Kulvinder  L. GCSE Maths tutor

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