Question

A balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 degree angle. Find the height of the balloon from the ground. ( imagine that there is no slack in the cable)

Answer 1

We can draw this situation as:

We can find h, the height of the balloon, by using the trigonometric ratio that tells us that the sine of an angle in a right triangle is equal to the ratio between its opposite side and the hypotenuse.

We can write this as:

`\begin{gathered} \sin (60\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(h)/(200) \\ h=200\cdot\sin (60\degree)\approx200\cdot0.866\approx173 \end{gathered}`

Answer: the height of the balloon is 173 m.