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 \[\Delta AED,\] |
\[\tan 30{}^\circ =\frac{AE}{ED}\] \[[\because ED=BC]\] |
\[\Rightarrow \]\[\frac{1}{\sqrt{3}}=\frac{108-h}{36\sqrt{3}}\]\[\Rightarrow \]\[108-h=36\] |
\[\Rightarrow \]\[h=108-36\]\[\Rightarrow \]\[h=72\,\,m\] |
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