Question

A balloon is connected to a meteorological station by a cable of length $200m$, inclined at ${60}^o$ to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the cable

• A. $173.2m$
• B. $192.35m$
• C. $123.25m$
• D. None of these

Answer 1

The correct option is A $173.2m$

Let $C$ be the position of the meteorological station, $B$ be the position of the balloon and $CB$ be the cable.

Let the height of the balloon from the ground be $AB=h$ metres.

From the $\Delta ACB$

$\frac{AB}{BC}=\sin {60}^{\circ }$

$\Rightarrow \frac{h}{200}=\frac{\sqrt{3}}{2}$

$\Rightarrow h=200\times \frac{\sqrt{3}}{2}$

$\Rightarrow h=100\sqrt{3}$

$\therefore h=100\times 1.732=173.2$ [since $\sqrt{3}=1.732$]

Hence, the height of the balloon above the ground is $173.2m$