Key Terms
- SAS: Two sides and the INCLUDED angle between them
- SSS: All three sides known, no angles
- Included angle: The angle that sits BETWEEN the two known sides
- Cosine rule: Generalised version of Pythagoras for any triangle
Must-Know Facts
- Use the cosine rule when: SAS (2 sides + included angle) or SSS (all 3 sides)
- Angle A is BETWEEN sides b and c in the formula
- When A = 90°, cos 90° = 0, so it simplifies to Pythagoras
- After finding cos A, use cos⁻¹ to get the angle
- Always check: the largest angle is opposite the longest side
Key Formulas
- Find side: a² = b² + c² − 2bc cos A
- Find angle: cos A = (b² + c² − a²) ÷ 2bc
- Use when: SAS or SSS
Common Mistakes
- Wrong angle pairing: In a² = b² + c² − 2bc cos A, angle A must be opposite side a
- Sign error with −2bc cos A: If angle A is obtuse, cos A is negative, so the term becomes positive — let the calculator handle this
- Finding angle — wrong rearrangement: Use cos A = (b² + c² − a²) ÷ 2bc, then cos⁻¹ to find A
- Using cosine rule when sine rule is simpler: If you have an angle-opposite-side pair, sine rule is usually easier
This topic summary covers Knowledge Organiser: The Cosine Rule within Cosine Rule for GCSE Mathematics. Revise Cosine Rule in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Cosine Rule
Which formula is the cosine rule for finding side a?
Show that when angle A = 90°, the cosine rule reduces to Pythagoras' theorem.
Quick recall flashcards
Cosine Rule
a² = b² + c² - 2bc cosA. Use for SAS or SSS. Like Pythagoras with a twist!
Cosine Rule
a² = b² + c² - 2bc cos A