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Question

The angle of elevation of the top of a hill at the foot of a tower is 60 and the angle of elevation of top of the tower from the foot of the hill is 30. If the tower is 50 m high, then the height of the hill is :

A
148 m
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B
150 m
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C
152 m
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D
160 m
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Solution

The correct option is C 150 m
Let AB be the hill and CD be the tower.
Since the angle of elevation of the top of the tower from the foot of the hill is 300.
CBD=300
Again, the angle of elevation of the top of the hill from the foot of the tower is 600.
ADB=600
In right-angled ΔBDC
tan300=CDBD
13=50BD
BD=503 m .....(i)
In right-angled ΔABD, we have
tan600=ABBD
3=AB503 ....{from (i)}
AB=3×503 ........(ii)
AB=150 m

391475_348303_ans_73cd3ecc97364f24a759f98db350f60c.png

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