O-LevelMathematicsTrigonometry4024/22 · Oct/Nov 2017 · Q1112 Marks
A vertical mast, XY, is positioned on horizontal ground. The mast is supported by four cables attached to the mast at P and to the ground at points A, B, C and D. Y is the centre of the square ABCD. PY = 7.50 m. [Figure of mast with cables and square base]
- (a)Given that AB = 3.65 m, show that AY = 2.58 m correct to 3 significant figures.[3]
- (b)Calculate the length of one of the cables used to support the mast.[2]
- (c)Calculate A P̂ B.[3]
- (d)(i)The angle of elevation of X from A is 77.0°. Calculate the height, XY of the mast.[2]
- (d)(ii)Calculate the angle of elevation of X from the midpoint of AB.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [3] (a) Need to see 2.58 rounded from a correctly obtained 2.581 or better.
- Method 1:
- M2 for AY = 3.65cos45 or (3.65÷2) ÷ sin 45
- or M1 for e.g. AY/3.65 = cos 45 or sin45 = (3.65÷2)/AY
- Method 2:
- M1 for such as AY² + AY² = 3.65² or 3.65² + 3.65² = AC² soi
- M1 for AY² = 3.65² / 2 oe
- A1 for AY = 2.580[9...]
- [2] (b) 7.93
- M1 for 7.52 + 2.582
- [3FT] (c) 26.6° or 2sin-1((0.5×3.65) / their7.93)
- or cos [...] = (their7.93² + their7.93² – 3.65²) / (2x their7.93²)
- Or M1 for sin[...] = (0.5×3.65) / their7.93
- or 3.65² = their7.93² + their7.93² – 2 ×their 7.93² × cos [...]
- [2] (d)(i) 11.18 or 11.2
- M1 for tan 77 = XY / 2.58 oe
- [2FT] (d)(ii) 80.7°
- M1 for tan [...] = (their 11.2) / (3.65÷2)
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