4MA1/1HR Jun 2024, Question 22: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
Using cuboid ABCDEFGH with AB = 8 cm, AD = 12 cm and DE = 20 cm, M the midpoint of base ADEH and P the midpoint of CF, find angle BMP to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1M is 8 cm below P and 6 cm across, so MP² = 6² + 8² = 100, MP = 10
- 2From B: 6, 10 across and 8 down to M, so BM² = 6² + 10² + 8² = 200
- 3From B to P: 12 and 10 across, same height, so BP² = 12² + 10² = 244
- 4cos BMP = (100 + 200 − 244) ÷ (2 × 10 × √200) = 0.19799…
- 5Angle BMP = cos⁻¹(0.19799…) = 78.6
Answer78.6
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