Question

Question 11
The angle of elevation of the top of a tower is ${30}^{\circ }$. If the height of the tower is doubled, then the angle of elevation of its top will also the doubled.

Answer 1

The statement is false.
Case I:
Let the height of the tower is h and BC = x m.

$tan{30}^{\circ }=\frac{AC}{BC}=\frac{h}{x}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x}\dots \dots \left(i\right)$



Case II

By condition, the height of the tower is doubled, i..e, PR = 2h.

In$\Delta PQR,tan\theta =\frac{PR}{QR}=\frac{2h}{x}$

$\Rightarrow tan\theta =\frac{2}{x}\times \frac{x}{\sqrt{3}}[\because h=\frac{x}{\sqrt{3}}fromEq.(i\left)\right]$

$\Rightarrow tan\theta =\frac{2}{\sqrt{3}}=1.15$

$\therefore \theta =ta{n}^{-1}\left(1.15\right)<{60}^{\circ }$

Hence, the required angle is not doubled.