Question

A captain of an aeroplane flying at an altitude of $1000$ metres sights two ships as shown in the figure. If the angle of depression are ${60}^o$ and ${30}^o$. Find the distance between the ships.

• A. $2210$ m
• B. $2196$ m
• C. $2219.7$ m
• D. $2309.3$ m

Answer 1

The correct option is D $2309.3$ m

Let $A$ be the position of the captain of an aeroplane flying at the altitude of $1000$ metres from the ground.
$AB=$ the altitude of the aeroplane from the ground $=1000$ m
$P$ and $Q$ be the position of two ships.
Let $PB=x$ metres and $BQ=y$ metres
Required: $PQ=$ Distance between the ships $=(x+y)$ metres
$\Rightarrow ABP$ is right angled $△$ at $B$,
$\Rightarrow \frac{AB}{PB}=\tan {60}^o$
$\Rightarrow \frac{1000}{x}=\sqrt{3}\Rightarrow x=\frac{1000}{\sqrt{3}}$
$\Rightarrow x=\frac{1000\left(1.732\right)}{3}=577.3$ m
$ABQ$ is rt. $△$ at $B$
$\Rightarrow \frac{AB}{BQ}=\tan {30}^o$
$\Rightarrow \frac{1000}{y}=\frac{1}{\sqrt{3}}\Rightarrow y=1000\sqrt{3}$
$\Rightarrow y=1000\left(1.732\right)=1732$ m
Required distance between the ships$=(x+y)$ metres
$=(577.3+1732)$ m $=2309.3$ m