4024/21 Oct/Nov 2025, Question 25: Trigonometry in 3D: Cuboids
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 6 marks
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The question, in short
Cuboid ABCDEFGH has EH = 12 cm, HG = 10 cm and GC = 7 cm, with diagonal CE drawn. Show the length of CE to 1 decimal place, then find the angle CE makes with base EFGH.
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Part (a) · 3 marks
Using the given edge lengths, show that the space diagonal CE equals 17.1 cm when rounded to 1 decimal place.
- 1EG² = 12² + 10² = 144 + 100 = 244
- 2CE² = 244 + 7² = 293
- 3CE = √293 = 17.117… = 17.1 cm (1 d.p.)
Answer17.11 to 17.12
Part (b) · 3 marks
Calculate the angle between the diagonal CE and the base EFGH.
- 1The angle is CEG (G is directly below C)
- 2sin CEG = 7/√293
- 3Angle CEG = 24.1…°
Answer24.1… or 24.2
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