O-LevelMathematicsTrigonometry4024/21 · May/June 2019 · Q118 Marks
The diagram shows the positions of two ports, A and B, and a lighthouse L. The bearing of B from L is 062°. AB = 13 km, BL = 14km and AL = 8km.
- (a)Calculate the bearing of A from L.[4]
- (b)A boat is located at C. C is 11 km from B and BCA = 90°. The boat travels to port A in a straight line. Find the distance the boat travels.[2]
- (c)The boat then travels in a straight line from port A to port B. It travels at an average speed of 3.75 km/h. Calculate the time taken for the boat to travel from port A to port B. Give your answer in hours and minutes.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [4] 128[.0]° or 128.03° to 128.04° B3 for 66[.0] or 66.03 to 66.04 or M2 for [cos L] = (14²+8²-13²)/(2×14×8) or M1 for 13² = 14² + 8² – 2 × 14 × 8 × cosL After 0 scored, SC1 for 62 + their BLA
- [2] 6.93 or 6.92 M1 for √13² – 11² isw
- [2] 3 hours 28 minutes M1 for 13/3.75
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