4MA1/2HR Jan 2021, Question 22: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Isosceles triangle ABC lies in a horizontal plane with T vertically above B; given AB = BC = 8 cm, angle ABC = 140°, TB = 10 cm and M the midpoint of AC, find the angle between MT and plane ABC, to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1AB = BC, so BM is perpendicular to AC and angle ABM = 140 ÷ 2 = 70°
- 2BM = 8 × cos 70° = 2.736… cm
- 3TB is vertical, so the angle needed is TMB: tan TMB = 10 ÷ 2.736… = 3.654…
- 4Angle TMB = tan⁻¹(3.654…) = 74.7
Answer74.7
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