question_answer

If the angle of elevation of a tower from a distance 100 m from its foot is \[30{}^\circ ,\] then the height of the tower is

[SSC (CGL) Mains 2014]

A) \[\frac{100}{\sqrt{3}}\,m\]

B) \[100\sqrt{3}\,m\]

C) \[\frac{50}{\sqrt{3}}\]                           

D) \[50\sqrt{3}\,m\]

Correct Answer: A

Solution :

Let the height of tower be h m.

\[\tan 30{}^\circ =\frac{AB}{BC}\]\[\Rightarrow \]\[\frac{1}{\sqrt{3}}=\frac{h}{100}\]

\[\Rightarrow \]   \[h=\frac{100}{\sqrt{3}}m\]

\[\therefore \] Height of the tower is \[\frac{100}{\sqrt{3}}m.\]