SATHEE: Quantitative Aptitude Ques 1867

Quantitative Aptitude Ques 1867

Question: There are two vertical posts, one on each side of a road, just opposite to each other. One post is 108 m high. From the top of this post, the angles of depression of the top and foot of the other post are $ 30{}^\circ $ and $ 60{}^\circ , $ respectively. The height of the other post, (in metre) is

Options:

A) 36

B) 72

C) 108

D) 110

Show Answer

Answer:

Correct Answer: B

Solution:

Let the height of other part be h m and distance between the post be x m. In $ \Delta ABC, $ $ \tan 60{}^\circ =\frac{AB}{BC} $
$ \Rightarrow $ $ \sqrt{3}=\frac{108}{BC} $

$ \Rightarrow $ $ BC=\frac{108}{\sqrt{3}}=36\sqrt{3}m $ In $ \Delta AED, $ $ \tan 30{}^\circ =\frac{AE}{ED} $ $ [\because ED=BC] $

$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{108-h}{36\sqrt{3}} $
$ \Rightarrow $ $ 108-h=36 $

$ \Rightarrow $ $ h=108-36 $
$ \Rightarrow $ $ h=72m $

Quantitative Aptitude Ques 1866

Quantitative Aptitude Ques 1868

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