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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.
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 `∠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
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