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Tuesday, 4 June 2013

Cosine Rule

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 formulae can be rearranged to give :
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

When to use it

We can use the cosine formula when we are given:
Two sides and an angle.
image: triangle
Three sides
Check whether your formula sheet gives these formulae in both formats. If it does not, you may need to rearrange them yourself.
Question
Find the length of BC.
Question
Find the size of angle R.
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