Question

From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stone on the same side of the aeroplane are observed to be 30${}^{\circ }$ and 60${}^{\circ }$ respectively. The height at which the aeroplane is flying in km is

• A. $2$
• B. $\frac{2}{\sqrt{3}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{4}{\sqrt{3}}$

Answer 1

Answer: (C)

Let the distance of two consecutive stones are $x,x+1$.
In $\Delta BCD$,

$\tan 60^{\circ }=\frac{h}{x}$
$\Rightarrow x=\frac{h}{\sqrt{3}}\dots (i)$
In $\Delta ABC$,
$\tan 30^{\circ }=\frac{h}{x+1}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+1}$
$\Rightarrow \frac{h}{\sqrt{3}}+1=\sqrt{3}h$ (From (i))
$\Rightarrow \frac{2h}{\sqrt{3}}=1$
$\Rightarrow h=\frac{\sqrt{3}}{2}km$