O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2022 · Q107 Marks
[Figure 10.1] The diagram shows the positions of three towns, P, Q and R. Q is on a bearing of 052° from P. PQ = 11.5 km, QR = 14.6 km and PR = 17.2 km.
- (a)Calculate the bearing of R from Q.[4]
- (b)A is a point on horizontal ground. The angle of elevation of the top of a vertical mast from A is 68°, correct to the nearest degree. The distance of the base of the mast from A is 45 m, correct to the nearest metre. Calculate the lower bound of the height of the mast.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [4] (a) 150.5 or 150.48 to 150.49; B3 for [∠PQR = ] 81.5[1...] OR M2 for (11.5² +14.6² -17.2²)/(2×11.5×14.6) oe or M1 for 17.2² =11.5² +14.6² -2×11.5×14.6cos[ ] oe M1 for 180 + 52 – their PQR oe
- [3] (b) 107.4...; B1 for 67.5 and 44.5 seen M1 for tan (their 67.5) = h/(their 44.5) oe
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