4MA1/2H Jan 2023, Question 23: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
For the pentagonal prism with AE = BC = x, AB = 2x, ED = CD = 8, right angles at A and B, 120° at E and D, and length 12, find the angle between AJ and base ABHG, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1D is above the middle of AB: horizontal ED = 8 cos 30° = 4√3, so x = 4√3
- 2Height of D above AB = x + 8 sin 30° = 4√3 + 4 = 10.93 cm
- 3M is the point on the base below J: AM = √(12² + (4√3)²) = √192 = 13.86 cm
- 4tan(angle) = JM/AM = 10.93 ÷ 13.86
- 5Angle = tan⁻¹(0.789) = 38.3°
Answer38.3
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