Question

State true(1) or false(0):The angle of elevation of the top of a tower is ${30}^0$. If the height of the tower is doubled, then the angle of elevation of its top will also be doubled.

Answer 1

The given angle of elevation $={30}^o.$

Let the height of the tower $=h$ and the viewer be at a distance of $x$ from the foot of the tower.

Then, $\frac{h}{x}=\tan {30}^o=\frac{1}{\sqrt{3}}$ ........(i)

If the height of the tower is doubled then the new height $=2h.$

Let the angle of elevation of the top be $\theta .$

Then, $\tan \theta =\frac{2h}{x}=2\times \frac{1}{\sqrt{3}}=\frac{2}{\sqrt{3}}$ ......(from i)...........(ii)

But if the angle of elevation doubles then it should be $=\theta ={2\times 30}^o={60}^o.$

Then, $\tan \theta =\tan {60}^o=\sqrt{3}$ ........(iii).

Comparing (ii) & (iii), there is a contradiction.

$\therefore$ The assertion is incorrect.