0580/23 Oct/Nov 2023, Question 21: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 6 marks
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The question, in short
Cuboid ABCDEFGH has AB = 14 cm, BC = 5 cm, CG = 8 cm; M is midpoint of HG. Find BM and the angle BM makes with base ABCD.
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Part (a) · 3 marks
Calculate the length BM, using the cuboid dimensions and M as midpoint of HG.
- 1BM² = (14/2)² + 5² + 8² = 49 + 25 + 64 = 138
- 2BM = √138 = 11.74… ≈ 11.7 cm
Answer11.7 or 11.74 to 11.75
Part (b) · 3 marks
Calculate the angle between line BM and the base ABCD.
- 1X is the midpoint of DC, directly below M, so the angle is MBX
- 2BX² = 5² + 7² = 74, so BX = 8.60…
- 3BM² = 74 + 8² = 138, so BM = 11.74…
- 4sin MBX = 8/11.74…, so angle MBX = 42.9°
Answer42.9 to 43.14
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