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A balloon is seen at the same time from three points A, B and C lying on a straight road vertically below it. The angle of elevation at B is double the angle of elevation at A, and the angle of elevation at C is triple the angle of elevation at A. If AB = 200 m and BC = 100 m, then the height of the balloon is

1. 50 metres
2. 50√3 metres
3. 50√2 metres
4. None of these

Correct answer: None of these

Solution

In triangle PAB the angles give PB=AB=200, and in triangle PBC the sine rule gives sin3a=2sin a, so a=30deg. Then h=200 sin(2a)=200 sin60=100*sqrt(3) m (about 173 m), which is not among the listed values, so 'None of these'.

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