4MA1/1H Jun 2021, Question 22: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
In a prism with triangular ends and horizontal base ABEF, using AC = BC = FD = ED = 12 cm, AB = 10 cm and BE = 15 cm, work out the angle AD makes with the base, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1M is the midpoint of FE; D is directly above M, so the angle needed is DAM
- 2FM = 10 ÷ 2 = 5, so AM = √(5² + 15²) = √250 = 15.81…
- 3Height DM = √(12² − 5²) = √119 = 10.91…
- 4tan DAM = 10.91… ÷ 15.81…
- 5Angle DAM = 34.6
Answer34.6
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