4MA1/2H Jun 2023, Question 22: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
Triangle ABC lies on horizontal ground with AB = 9 m, BC = 11 m, AC = 16 m, and vertical flagpole BF = 10 m at B. D is on AC with angle BDC = 90°. Find the angle of elevation of F from D, to one decimal place.
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Solution · 5 marks
- 1Cosine rule in triangle ABC: 9² = 11² + 16² − 2 × 11 × 16 × cos BCA
- 2cos BCA = (121 + 256 − 81) ÷ (2 × 11 × 16) = 296 ÷ 352 = 0.840909
- 3BCA = 32.765°
- 4BD is perpendicular to AC, so BD = 11 × sin 32.765° = 5.9525 m
- 5The angle of elevation is tan⁻¹(BF ÷ BD) = tan⁻¹(10 ÷ 5.9525)
- 6The angle of elevation of F from D is 59.2°
Answer59.2
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