4MA1/2HR Jan 2022, Question 19: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks
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The question, in short
A rectangular field ABCD has a vertical pole AE at corner A, with AE = 12 m, AB = 18 m and AD = 8 m. Find the angle between EC and the horizontal plane ABCD, to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1AD = 8 m, AB = 18 m, so AC = √(8² + 18²) = √(64 + 324) = √388 ≈ 19.697
- 2AE = 12 m, so tan(∠ECA) = AE / AC = 12 / √388
- 3∠ECA = tan⁻¹(12 / √388) ≈ tan⁻¹(12 / 19.697) ≈ tan⁻¹(0.609)
- 4∠ECA ≈ 31.4
Answer31.4
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