From a point P on a level ground, the angle of elevation of the top tower is 30º. If the tower is 100 m high, the distance of point P from the foot of the tower is.
A. 149 m B. 156 m C. 173 m D. 200 m Answer: Option CShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{Let AB be the tower.}\\
\text{Then,}\ \angle\text{APB}=30^{\circ}\\
\text{and AB}=100\ \text{m}\\
\frac{\mathrm{\text{AB}}}{\mathrm{\text{AP}}}=\tan30^{\circ}=\frac{\text{1}}{\sqrt{\text{3}}}\\
\Rightarrow\mathrm{AP}=(\mathrm{AB}\times\sqrt{3})\mathrm{m}\\
=100\sqrt{3}\mathrm{~m}\\
=(100\times1.73)\mathrm{m}\\
=173\mathrm{~m}.\end{array}$
