A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that Q R = 15 m . If from a point A on the ground the angle of elevation of R is 60 ° and the part P R of the tower subtends an angle of 15 ° at A , then the height of the…

Question

A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that Q R = 15 m . If from a point A on the ground the angle of elevation of R is 60 &#176; and the part P R of the tower subtends an angle of 15 &#176; at A , then the height of the tower is

Aicharya · Accepted Answer

Plotting the diagram of the given values we get,
From the right triangle $R Q S,$
$\tan 60 ° = \frac{15}{a}$
$a = \frac{15}{\sqrt{3}} = 5 \sqrt{3}$
In right triangle $P Q S,$
$\tan 75 ° = \frac{h}{a}$
$\Rightarrow \frac{h}{5 \sqrt{3}} = 2 + \sqrt{3}$
$\Rightarrow h = 10 \sqrt{3} + 15$
$\Rightarrow h = 5 (2 \sqrt{3} + 3)$

A tower P Q stands on a horizontal ground with base Q on the ground. The point R divides the tower in two…

Solution