The Cosine Rule | Revision

Download The Revision Sheet Here: Cosine Rule Revision Sheet (The formatting looks nicer)

The cosine rule applies to any given triangle. You do not need a right angle.





This rule is used when:

  • You know two sides of the triangle and the angle between them (SAS | Side Angle Side)
  • Or when you are given three sides of the triangle and want to work out an angle (SSS | Side Side Side)

The formula:

  • When you are looking for a missing side of a triangle, use this version: a2 = b2+ C2 – 2bcCosA
  • When you are looking for a missing angle, use this version: CosA = b2 + c2 – a2 / 2bc

Example Question:

Q1) PRS is a triangle. Work out the length of the diagonal PR (3 marks)

The triangle above is not a right-angled triangle so using SOH CAH TOA will not work.

In this question, we know two sides and including the angle, meaning we can use the cosine rule.

We substitute the values we know into the cosine rule formula and use a calculator to work out the answer, we then square root that answer to get your final result.

The reason why we round to three significant figures is to achieve the same degree of accuracy as the original measurements.

Another Example Question:

Q2) Triangle PQR has sides of 9cm, 10cm and 14cm. Work out the size of the smallest angle.

Note: The smallest angle is always opposite the smallest side.


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