DfE statement G22 · Geometry and measures
The sine rule and the cosine rule
The sine rule and the cosine rule is content statement G22 of the DfE GCSE mathematics subject content, in the geometry area. It is Higher tier only, and it is normally a calculator-paper question. Below is what the specification actually requires, the 4 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Know and apply the sine rule, a/sin A = b/sin B = c/sin C, and cosine rule, a² = b² + c² − 2bc cos A, to find unknown lengths and angles." (statement G22). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.
Calculator
This is calculator work, which places it on Papers 2 and 3. Know your own calculator before the exam, keep full accuracy through the working and round only at the end.
Common mistakes
- Using the sine rule when the given information is two sides and the angle between them. SAS needs the cosine rule.
- Missing the second, obtuse solution when the sine rule gives an angle and the diagram allows either.
- In the cosine rule, subtracting before multiplying: b² + c² − 2bc cos A means the whole 2bc cos A term is subtracted, computed last.
- Pairing a side with an angle that is not opposite it.
Formulae for this statement
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is the sine rule and the cosine rule on Foundation or Higher?
Higher only. Foundation papers do not ask for it.
Can I use a calculator for the sine rule and the cosine rule?
Yes, on Papers 2 and 3, which are the calculator papers and where questions on this usually sit. Paper 1 is non-calculator.
Which rule do I use, and when?
Use the sine rule when you have a side and its opposite angle, plus one more piece of information. Use the cosine rule when you have two sides and the angle between them (SAS) or all three sides and want an angle. Neither is on the formulae sheet, so both must be known, and both are Higher tier.
What is the single most common mistake here?
Using the sine rule when the given information is two sides and the angle between them. SAS needs the cosine rule.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Geometry and measures at Foundation or at Higher.