A balloon is connected to a meteorological ground station by a cable of length
Question:

A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

Solution:

Let AB be the balloon of height h. And the balloon is connected to the metrological ground station by a cable of length 215 m. Let AC = 215 and

Here we have to find height of balloon.

We have the following corresponding figure

So we use trigonometric ratios

In a triangle ABC,

$\Rightarrow \quad \sin C=\frac{A B}{A C}$

$\Rightarrow \quad \sin 60^{\circ}=\frac{h}{215}$

$\Rightarrow \quad \frac{\sqrt{3}}{2}=\frac{h}{215}$

$\Rightarrow \quad h=186$

Hence the height of balloon is $186 \mathrm{~m}$.