4MA1/1HR Jan 2023, Question 21: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
In triangular prism ABCDEF with rectangular base ABCD, AB = 6 cm, DE = 2.2 cm, angle DAE = 18° and angle ADE = 90°, find the angle between BE and plane ABCD, to one decimal place.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1In triangle ADE: AD = 2.2 ÷ tan 18° = 6.771 cm
- 2In the base, triangle ABD: BD = √(6.771² + 6²) = 9.047 cm
- 3The required angle is EBD: tan EBD = 2.2 ÷ 9.047
- 4Angle EBD = tan⁻¹(0.2432) = 13.7°
Answer13.7
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