0580/41 Oct/Nov 2025, Question 27: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 4 marks
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The question, in short
Prism with trapezium cross-section ABCD, right angles at A and D, AB = 10 cm, AD = 5 cm, DC = 7 cm, length 15 cm. Find the angle diagonal AG makes with base ABFE.
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Solution · 4 marks
- 1G is 5 cm above the base; its foot is 7 cm along AB and 15 cm along the length from A
- 2Distance from A to the foot = √(15² + 7²) = √274 = 16.55… cm
- 3tan θ = 5/√274
- 4θ = 16.80… ≈ 16.8°
Answer16.8 or 16.80 to 16.81
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