O-LevelMathematicsTrigonometry4024/21 · Oct/Nov 2019 · Q912 Marks

The diagram shows the positions of three farms A, B and C on horizontal ground. Farm B is on a bearing of 125° from farm A. AB = 950 m, BC = 680 m and AC = 520 m. [Figure 9 Diagram of farms A, B, C with bearing and distances]

(a)Show that BẬC = 44.0°, correct to 1 decimal place.[3]
(b)Calculate the bearing of A from C.[1]
(c)Calculate the time it takes for Amira to walk from A to the point that is closest to farm C. Give your answer in minutes and seconds, correct to the nearest second.[4]
(d)A helicopter hovers vertically above farm B. The angle of elevation of the helicopter from farm A is 10.7°. Calculate the angle of elevation of the helicopter from farm C.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[3] cos BẬC = (950² + 520² - 680²)/(2 × 950 × 520) M2 or M1 for 680² = 950² + 520² - 2 × 950 × 520 × cos BẬC oe BẬC = 44.01 to 44.02 [= 44.0°] A1
[1] 349
[4] 4 min 53 s M2 for [distance = ]520 cos44 or M1 for cos 44 = d/520 oe AND M1 for their distance ÷ 4.6
[4] 14.8° or 14.78 to 14.79 M2 for h = 950 tan 10.7 oe or M1 for tan10.7 = h/950 oe AND M1 for tan[ ]= their h/680 oe

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