Question

A boy, 1.6 m tall, is 20 m away from a tower and observes the angle of elevation of the top of the tower to be (i) ${45}^0$(ii) ${60}^0$. Find the height of the tower in each case.

Answer 1

Let's consider the height of the tower to be ${}^{\prime }{h}^{\prime }$ m.
(i) Here, $\theta ={45}^0$
$tan{45}^0=(h-1.6)/20$
$1=(h-1.6)/20$
$h=21.6m$
Thus, the height of the tower is $21.6m$.
(ii) Here, $\theta ={60}^0$
$tan{60}^0=(h-1.6)/20$
$\sqrt{3}=(h-1.6)/20$
$h=20\times \sqrt{3}+1.6=36.24m$
Thus, the height of the tower is $36.24m.$