Question

A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 600 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 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 `∠ACB = 60^@`

Here we have to find the height of balloon.

We have the following corresponding figure

So we use trigonometric ratios 

In a triangle ABC

`=> sin C = (AB)/(AC)`

`=> sin 60^@ = h/215`

`=>  sqrt3/2 = h/215`

`=> h = 186`

Hence the height of balloon is 186 m