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Question

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45. The angle of elevation of the top of the same tower from a point B, due south of A is 30. If the distance between A and B is 542 m, then the height of the tower (in metres), is

A
108
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B
543
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C
363
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D
54
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Solution

The correct option is D 54
According to the question the figure is

Now from the figure
OA=hOB=3hOB2=OA2+AB23h2=h2+(542)2h=54m

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