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From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be \( \Large 30 ^{\circ} \) and \( \Large 45 ^{\circ} \), respectively. What is the height of the tower?

A) 400 m
B) \( \Large 400\sqrt{3} \) m
C) \( \Large \frac{400}{\sqrt{3}} \) m
D) None of these

Correct Answer:




D) None of these

Description for Correct answer:
Let AE = 200 m be the height of the cliff

and BD = h be the height of the tower,

and x is the distance between cliff and tower.

In \( \Large \triangle ABC \)

\( \Large \tan 30 ^{\circ} =\frac{200-h}{x}=\frac{1}{\sqrt{3}}=\frac{200-h}{x} \)

=> \( \Large x = \left(200 - h\right)\sqrt{3} \) ...(i)

And in \( \Large \triangle ADE, \tan 45 ^{\circ} = \frac{200}{x} \)

=> \( \Large 1 = \frac{200}{x} => x = 200 m \)

From Eq. (ii), \( \Large 200= \left(200-h\right)\sqrt{3} \)

=> \( \Large h = 200 \left(\frac{\sqrt{^{3}-1}}{\sqrt{3}}\right) m \)

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

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