From a point on the ground, the angle of elevation of the top of a tower is observed to be   From a point   vertically above the first point of observation, the angle of elevation of the top of the tower is  ,then the height of the tower and its horizontal distance from the point of observation is

detailed solution

Correct option is D

Given that from a point on the ground, the angle of elevation of the top of a tower is observed to be   From a point   vertically above the first point of observation, the angle of elevation of the top of the tower is  .
Consider the diagram,
 We know,
$\mathit{tan\theta }=\frac{\mathit{Perpendicular}}{\mathit{Base}}$
$\mathit{tan}60°=\sqrt{3}$
$\mathit{tan}30°=\frac{1}{\sqrt{3}}$,
In triangle QAP,
$\mathit{tan}60°=\frac{\mathit{QP}}{\mathit{AP}}$
$\Rightarrow \mathit{tan}60°=\frac{x+40}{\mathit{AP}}$
In triangle QBP,
$\mathit{tan}30°=\frac{\mathit{QR}}{\mathit{BR}}$
$\Rightarrow \mathit{tan}30°=\frac{x}{\mathit{BR}}$
Therefore,
 
As AP and BR are equal so equate the expression of both to each other and find x.  
Now,
 
Again,
$d=\frac{20}{\mathit{tan}30°}$
$\Rightarrow d=\frac{20}{\frac{1}{\sqrt{3}}}$
$\Rightarrow d=20\sqrt{3}\mathit{ m}$
Distance between point and tower   and the height of the tower is 60 m.
Therefore, option 4 is correct.