0580/21 May/Jun 2024, Question 21: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks
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The question, in short
Cuboid with HD = 4 cm, EH = 6.5 cm, EF = 9.1 cm; find the angle between the space diagonal CE and the base CDHG.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1The angle between CE and the base is angle ECH (E is above H)
- 2HG = EF = 9.1, so CH = √(4² + 9.1²) = √98.81 = 9.940…
- 3tan ECH = EH/CH = 6.5/9.940…
- 4Angle = tan⁻¹(0.6539…) = 33.18… ≈ 33.2°
Answer33.2 or 33.18…
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