| | Question 47

There are two towers, one on each side of the road just opposite to each other. One tower is 54m high. From the top of this tower, the angles of the depression of the top and foot of the other tower are 30 and 60 respectively. The height of the other tower is:
(A) 30m
(B) 32m
(C) 36m
(D) 42m


Answer: (C)

Explanation:
AB and CD are Towers.
BD is the width of the road.
AB = 54 m
In ∆ AEC
tan 30 = AE/EC = 1/√3
=> AE : EC = 1 : √3
In ∆ABD
tan 60 = AB/BD
√3 = AB/BD
=> AB : BD = √3 : 1
From diagram we know EB = CD and EC = BD
Now,

AB     :     BD     :     AE
             √3           1
√3     :      1
3      :     √3     :     1

CD = AB – AE = 3 – 1 = 2 units

3 units of AB -> 54 m
1 unit -> 18
Then 2 units -> 36 m
Hence, the height of the other tower is 36m.

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