0580/42 May/Jun 2025, Question 27: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 4 marks
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The question, in short
Cube with base ABCD and P directly above C; calculate the angle between diagonal AP and the base ABCD.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Let the side be 1: AC = √(1² + 1²) = √2
- 2The angle between AP and the base is angle PAC, with PC = 1
- 3tan PAC = 1/√2
- 4Angle PAC = 35.26… ≈ 35.3°
Answer35.3 or 35.26…
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Also searched as: 0580/42/M/J/25 · 0580_s25_qp_42 · 0580 s25 42 · question 27.
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