4MA1/2H Nov 2021, Question 18: The Cosine Rule
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Quadrilateral ABCD with diagonal AC: use the cosine rule and ½ab sin C with AB 9, BC 12, CD 7 cm and angles 60° and 84° to find the total area.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Cosine rule: AC² = 9² + 12² − 2 × 9 × 12 × cos 60° = 117
- 2Area ABC = 1/2 × 9 × 12 × sin 60° = 46.76…
- 3Area ACD = 1/2 × 7 × √117 × sin 84° = 37.65…
- 4Total = 46.76… + 37.65… = 84.4 cm²
Answer84.4
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