4PM1/02R Jun 2022, 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 a square base and all edges equal; find the angle between plane CVD and base ABCD, in degrees to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Let every edge be a. Let X be the midpoint of CD and O the centre of the base; the angle is VXO
- 2CX = a/2, so VX² = a² − (a/2)², VX = (√3/2)a
- 3OX = a/2
- 4cos θ = OX/VX = (a/2)/((√3/2)a) = 1/√3
- 5θ = 54.7°
Answer54.7°
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