MA30-07 Maths Coming soon
The cosine rule
MA30-07
This lesson is coming soon.
In this lesson
Use the cosine rule to find a missing side in any triangle, and rearrange the cosine rule to find a missing angle from three known sides - a distinct algebraic skill from finding a side.
What it covers
- State the cosine rule a^2 = b^2+c^2-2bc cosA (provided on the exam formula sheet, so substitution accuracy matters more than memorisation)
- Use the cosine rule to find a missing side when two sides and the included angle are known
- Rearrange the cosine rule to isolate cosA when all three sides are known, then use inverse cosine to find the angle
- Substitute the correct angle/side from the diagram (avoiding the documented 'used the wrong angle' error) and correctly attach a calculated angle back to the correct vertex
Key words
For: Edexcel IGCSE 4MA1, Cambridge IGCSE 0580, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| Edexcel IGCSE 4MA1 | H4.8C | Understand and use the sine and cosine rules for any triangle |
| Cambridge IGCSE 0580 | C6.5 | Extended content only. |
| Cambridge IGCSE 0580 | E6.5 | Use the sine and cosine rules in calculations involving lengths and angles for any triangle. |
| AQA GCSE 8300 | G22 | Know and apply the sine rule, a/sinA = b/sinB = c/sinC and cosine rule, a² = b² + c² - 2bc cosA to find unknown lengths and angles |
| Edexcel GCSE 1MA1 | G22 | 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 |
| Eduqas GCSE C300 | HG22 | 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 |
| OCR GCSE J560 | 10.05e | Know and apply the cosine rule, a^2 = b^2 + c^2 - 2bc cos A, to find lengths and angles. |
| OCR GCSE J560 | 10.05d | Know and apply the sine rule, a/sin A = b/sin B = c/sin C , to find lengths and angles. |
For teachers
This GCSE Maths lesson teaches the cosine rule. By the end, students should be able to use the cosine rule to find a missing side in any triangle, and rearrange the cosine rule to find a missing angle from three known sides - a distinct algebraic skill from finding a side. It works through three worked examples and the mistakes examiners report.