question_answer

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                                        [SSC (10+2) 2012]

A) 36                                

B) 72    

C) 108                              

D) 110

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  \[\Delta AED,\]

\[\tan 30{}^\circ =\frac{AE}{ED}\]                    \[[\because ED=BC]\]

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

\[\Rightarrow \]\[h=108-36\]\[\Rightarrow \]\[h=72\,\,m\]