Question

The angle of elevation $\theta$ of a vertical tower from a point on the ground is such that its tangent is $\frac{5}{12}$. On walking $192$ meters towards the tower in the same straight line the tangent of angle of elevation $\varphi$ is found to be $\frac{3}{4}$. Find the height of the tower

• A. $170$ m
• B. $175$ m
• C. $180$ m
• D. $185$ m

Answer 1

Answer: (C)

$180$ m

In $\Delta PQR,\tan \theta =\frac{h}{192+x}=\frac{5}{12}$
$\Rightarrow x=\frac{1}{5}(12h-960)$ ...(i)
In $\Delta PQS,\tan \varphi =\frac{h}{x}=\frac{3}{4}$
$\Rightarrow x=\frac{4h}{3}$ ...(ii)
From (i) and (ii), we get
$\frac{4h}{3}=\frac{1}{5}(12h-960)$
$\Rightarrow h=180$
$\therefore$ The height of the tower is 180 m