4PM1/02R Jun 2025, Question 6: Trigonometry in 3D: Pyramids and Cones
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks
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The question, in short
Right pyramid VABCD has rectangular base ABCD and AD = VC = 3AB. Find, to one decimal place in degrees, the angle between plane CVD and base ABCD.
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Solution · 6 marks
- 1Let AB = y, so AD = VC = 3y
- 2Let X be the midpoint of CD and O the centre of the base: angle VXO is required
- 3OX = 3y/2, CX = y/2
- 4VX = √((3y)² − (y/2)²) = (√35/2)y
- 5cos θ = OX/VX = (3y/2)/((√35/2)y) = 3/√35
- 6θ = 59.5°
Answer59.5°
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