4024/22 May/Jun 2022, Question 9: Choosing the Right Trigonometric Ratio
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks
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The question, in short
Right-angled triangle PQR with vertical pole PQ, PR = 20 m and RQ = 11 m; find PQ, then angles and lengths for ropes to points S and T.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Use Pythagoras in right-angled triangle PQR with PR = 20 and RQ = 11 to show PQ = 16.70 m to 2 decimal places.
- 1PQ² = 20² − 11² = 400 − 121 = 279
- 2PQ = √279 = 16.703…
- 3= 16.70 m (2 d.p.)
Answer16.703…
Part (b) · 5 marks
With RS = 30 m and angle of elevation of P from S equal to 36°, calculate angle RQS.
- 1tan 36° = 16.70/QS
- 2QS = 16.70 ÷ tan 36° = 22.98… m
- 3cos RQS = (11² + 22.98…² − 30²)/(2 × 11 × 22.98…)
- 4= −0.4957…
- 5Angle RQS = 119.7°
Answer119.6 to 119.8
Part (c) · 4 marks
In triangle PQT, PQ = 16.70, angle TPQ = 40° and angle PQT = 97°; calculate PT.
- 1Angle PTQ = 180 − 40 − 97 = 43°
- 2PT/sin 97° = 16.70/sin 43°
- 3PT = 16.70 × sin 97° ÷ sin 43°
- 4= 24.30… ≈ 24.3 m
Answer24.3
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