SATHEE: Quantitative Aptitude Ques 370

Quantitative Aptitude Ques 370

Question: From the top of a 60 m high tower, the angle of depression of the top and the bottom of a building are observed to be $ 30{}^\circ $ and $ 60{}^\circ $ respectively. The height of the building is

Options:

A) $ 60\sqrt{3} $

B) $ 40\sqrt{3} $

C) 40 m

D) 20 m

Show Answer

Answer:

Correct Answer: C

Solution:

Let DC is the tower and AB is the building. In $ \Delta ADE, $ $ \tan 30{}^\circ =\frac{60-h}{x} $

$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{(60-h)}{x} $

$ \Rightarrow $ $ x=(60-h)\sqrt{3} $ … (i)
Now, in $ \Delta BDC, $
$ \tan 60{}^\circ =\frac{60}{x} $
$ \Rightarrow $ $ \sqrt{3}=\frac{60}{x} $

$ \Rightarrow $ $ x\sqrt{3}=60 $

$ \Rightarrow $ $ [(60-h)\sqrt{3}],\sqrt{3}=60 $ [from Eq.(i)]

$ \Rightarrow $ $ (60-h)\times 3=60 $

$ \Rightarrow $ $ 60-h=20 $

$ \Rightarrow $ $ h=60-20=40 $

$ \therefore $ $ h=40,m $ So, height of the building is 40 m.

Quantitative Aptitude Ques 369

Quantitative Aptitude Ques 371

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