0580/22 Feb/Mar 2021, Question 23: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
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The question, in short
Pyramid VABCD has rectangular base ABCD, with V above the diagonal intersection M. Given AB = 12 cm, BC = 10 cm and VC = 14 cm, find the angle between VC and the base.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1The angle is VCM (between VC and MC)
- 2AC = √(10² + 12²) = √244 = 15.62…
- 3MC = 1/2 × 15.62… = 7.810…
- 4cos VCM = 7.810… ÷ 14
- 5Angle VCM = 56.09… ≈ 56.1°
Answer56.1 or 56.09…
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