Question

The angles of elevations of the tops of vertical towers as seen from the midpoint of the line joining the feet of the towers are ${60}^0$ and ${30}^0$ respectively. The ratio of the heights of the towers is :

• A. $2:1$
• B. $\sqrt{3}:1$
• C. $3:2$
• D. $3:1$

Answer 1

The correct option is D $3:1$

Let's say $AC=2x$, $h_1$ and $h_2$ be the heights of the towers and M be the midpoint of AC.

From $△ABM$,
$\frac{h_1}{x}=\tan {60}^0=\sqrt{3}$
so $h_1=x\times \sqrt{3}$

From $△CDM$,
$\frac{h_2}{x}=\tan {30}^0=\frac{1}{\sqrt{3}}$

$\Rightarrow h_2=\frac{x}{\sqrt{3}}$
$\therefore \frac{h_1}{h_2}=\frac{\sqrt{3}x}{x/\sqrt{3}}=3$
$\therefore h_1:h_2:=3:1$