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Two poles of equal heights stand on either side of a 100 m wide road. At a point between the poles the angles of elevation of the tops of the poles are \( \Large 30 ^{\circ} \) and \( \Large 60 ^{\circ} \). The height of each pole is:

A) 25m
B) \( \Large 25\sqrt{3} m \)
C) \( \Large \frac{100}{\sqrt{3}} m \)
D) none of these

Correct Answer:


B) \( \Large 25\sqrt{3} m \)

Description for Correct answer:
Let the height of pole AD = BC = h

In \( \Large \triangle OBC \tan 60 ^{\circ} = \frac{h}{x} \)

=> \( \Large x = \frac{h}{\sqrt{3}} \)

In \( \Large \triangle AOD \tan 30 ^{\circ} = \frac{h}{100-x} \)

=> \( \Large h = \left(100 - x\right) \frac{1}{\sqrt{3}}

= \left(100 - \frac{h}{\sqrt{3}}\right) \frac{1}{\sqrt{3}} \) [from (i)]

=> \( \Large 3h = 100\sqrt{3} - h \)

=> \( \Large h = \frac{100\sqrt{3}}{4} \)

=> \( \Large h = 25\sqrt{3} m \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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