4024/21 Oct/Nov 2022, Question 10: The Cosine Rule
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks
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The question, in short
Use triangle PQR with PQ = 11.5 km, QR = 14.6 km, PR = 17.2 km and Q on a bearing of 052° from P to find the bearing of R from Q, then find a lower bound for a mast height.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 4 marks
Calculate the bearing of R from Q using the given triangle side lengths and the bearing of Q from P.
- 1cos PQR = (11.5² + 14.6² − 17.2²)/(2 × 11.5 × 14.6)
- 2= 49.57/335.8 = 0.14762…
- 3Angle PQR = 81.51…°
- 4Bearing of P from Q = 52 + 180 = 232°
- 5Bearing of R from Q = 232 − 81.51… = 150.48… ≈ 150.5°
Answer150.5 or 150.48 to 150.49
Part (b) · 3 marks
Given angle of elevation 68° and base distance 45 m, both rounded, calculate the lower bound of the vertical mast height.
- 1Lower bound of angle = 67.5°, lower bound of distance = 44.5 m
- 2tan 67.5° = h/44.5
- 3h = 44.5 × tan 67.5° = 107.4… m
Answer107.4…
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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 10.
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