Question: Two poles of equal heights are standing opposite to each other on either side of a road which is 100 m wide from a point between them on road. Angles of elevation of their tops are $ 30{}^\circ $ and $ 60{}^\circ $ The height of each pole in metre) is
Options:
A) $ 25\sqrt{3} $
B) $ 20\sqrt{3} $
C) $ 28\sqrt{3} $
D) $ 30\sqrt{3} $
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Answer:
Correct Answer: A
Solution:
- Let the height of two poles be h m each.
Given, distance between two poles $ =100m $
Let the distance of first pole from the point $ =xm $
Then, the distance of second pole from the point
$ =(100-x)m $
In $ \Delta ABO, $ $ \tan 30{}^\circ =\frac{h}{x} $
$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{h}{x}=\sqrt{3}h=x $
(i)
From $ \Delta DOC, $ $ \tan 60{}^\circ =\frac{h}{100-x} $
$ \Rightarrow $ $ \sqrt{3}=\frac{h}{100-x} $
$ \Rightarrow $ $ \sqrt{3}(100-x)=h $
$ \Rightarrow $ $ \sqrt{3}(100-\sqrt{3}h)=h $ [from Eq. (i)]
$ \Rightarrow $ $ 100\sqrt{3}-3h=h $
$ \Rightarrow $ $ 4h=100\sqrt{3} $
$ \Rightarrow $ $ h=25\sqrt{3}m $
BETA
