Question

A balloon is connected to a meteorological ground station by a cable of length $215\text{m}$ inclined at ${60}^{\circ }$ to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

Answer 1

Let $AB$ be the height of the balloon.

In right angled $△ABC,$

$\sin {60}^o=\frac{AB}{AC}$

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

$\therefore$ $h=\frac{215\sqrt{3}}{2}m=186.2m$ $(Take\sqrt{3}=1.73)$

$\therefore$ height of the balloon from the ground is $186.2m$.