0580/23 Oct/Nov 2021, Question 23: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 6 marks
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The question, in short
For a triangular prism with right-angled end face BPC and given lengths AB = 12 cm, BP = 5 cm, PC = 4 cm, find a diagonal length and an angle with the base.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Work out the length AC using the prism's dimensions.
- 1AP² = 12² + 5² = 169, AP = 13
- 2AC² = 13² + 4² = 185
- 3AC = √185 = 13.6 cm
Answer13.6 or 13.60…
Part (b) · 3 marks
Determine the angle that AC makes with the base ABPQ.
- 1The angle is angle CAP
- 2tan CAP = 4/13
- 3angle CAP = tan⁻¹(4/13) = 17.1°
Answer17.1 or 17.08 to 17.10…
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Also searched as: 0580/23/O/N/21 · 0580_w21_qp_23 · 0580 w21 23 · question 23.
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