4024/22 Oct/Nov 2021, Question 10: Trigonometry in 3D: Cuboids
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks
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The question, in short
Field ABCD on horizontal ground with given bearings and lengths AD = 290 m, BD = 350 m; find the bearing of D from B, then the elevation angle of a mast at D as seen from C.
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Part (a) · 4 marks
Calculate the bearing of D from B using the given bearings from A and the triangle ABD.
- 1Angle BAD = 125 − 70 = 55°
- 2sin ABD = 290 × sin 55/350 = 0.6787…
- 3Angle ABD = 42.74…°
- 4Bearing of A from B = 70 + 180 = 250°
- 5Bearing of D from B = 250 − 42.74… = 207.25… ≈ 207.3°
Answer207.2 to 207.3
Part (b) · 5 marks
A vertical mast stands at D; its top has elevation 10° from A. Calculate the elevation angle of the same top from C.
- 1Angle DBC = 207.25… − 180 = 27.25…°
- 2CD = 350 × sin 27.25… = 160.28… m
- 3Height of mast = 290 × tan 10 = 51.13… m
- 4tan θ = 51.13…/160.28… → θ = 17.69… ≈ 17.7°
Answer17.6 to 17.8…
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