4MA1/2H Jun 2025, Question 24: Trigonometry in 3D: Pyramids and Cones
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Pyramid ABCDE has a square base ABCD, apex E above centre M, Q midpoint of AB, angle EQM = 80°, and EA : AB = n : 1. Find n to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Let AB = 1, so MQ = AQ = 0.5
- 2In right triangle EMQ: EQ = 0.5 ÷ cos80° = 2.879…
- 3In right triangle EQA: EA² = EQ² + AQ² = 2.879…² + 0.5²
- 4EA² = 8.540…, so EA = 2.922…
- 5EA : AB = 2.922… : 1
- 6n = 2.92
Answer2.92
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