4MA1/2HR Jun 2019, Question 23: Trigonometry in 3D: Pyramids and Cones
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 6 marks
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The question, in short
A square-based pyramid has base side 10 cm, apex A above centre O, equal slant edges, and total surface area 360 cm². Find the angle between edge AC and the base, to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Surface area: 100 + 4 × ½ × 10 × h = 360, so the height of each triangle h = 13
- 2Triangle height and half the side give AO = √(13² − 5²) = 12
- 3OC is half the diagonal: OC = √(10² + 10²) ÷ 2 = 7.07…
- 4Angle ACO = tan⁻¹(12 ÷ 7.07…) = 59.5°
Answer59.5°
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