O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2021 · Q109 Marks
ABCD is a field on horizontal ground. The bearing of B from A is 070°. The bearing of D from A is 125°. C is due south of B and due east of D. AD = 290 m and BD = 350 m. [Figure showing points A, B, C, D in a field with North direction. AD=290m, BD=350m, angle ADC right angle. NOT TO SCALE]
- (a)Calculate the bearing of D from B.[4]
- (b)A vertical mast is positioned at D. The angle of elevation of the top of the mast from A is 10°. Calculate the angle of elevation of the top of the mast from C.[5]
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Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [4] B1 for ∠BAD = 55 soi nfww M2 for sin[∠ABD] = (290sin(their55))/350 oe or M1 for 350/sin(their55) = 290/sin[∠ABD] oe
- [5] M1 for CD = 350 sin (70 – their 42.7) oe or 350 sin (their (a) – 180) oe AND M3 for tan = 290 tan 10 / their CD or M2 for [height of mast =] 290 tan 10 or M1 for tan 10 = [...]/290
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