0580/43 Oct/Nov 2025, Question 24: Trigonometry in 3D: Cuboids
Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 6 marks
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The question, in short
Cuboid ABCDEFGH has AE = 6.4 cm, EH = 5.1 cm and space diagonal AG = 13 cm. Find the missing edge EF and the angle AG makes with base EFGH.
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Part (a) · 3 marks
Work out the length of edge EF using the given dimensions and the space diagonal.
- 1AG² = EF² + EH² + AE²
- 2EF² = 13² − 6.4² − 5.1² = 169 − 40.96 − 26.01 = 102.03
- 3EF = √102.03 = 10.1 cm
Answer10.1 or 10.10…
Part (b) · 3 marks
Determine the angle between line AG and the plane of the base EFGH.
- 1The angle is AGE, with AE vertical
- 2sin AGE = 6.4/13
- 3angle AGE = 29.5°
Answer29.5 or 29.49… to 29.54…
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