A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
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Solution
Let the initial position A of balloon change to B after some time and CD be the girl.
In ΔACE,
AE/CE = tan 60º
(AF - EF)/(CE) = tan 60º
`(88.2 - 1.2)/(CE) = sqrt3`
`87/(CE) = sqrt3`
`CE = 87/sqrt3 = 29sqrt3 m`
In ΔBCG,
(BG)/(CG) = tan 30º
`(88.2-1.2)/(CG) = 1/sqrt3`
`87sqrt3 m = CG`
Distance travelled by balloon = EG = CG − CE
`= (87sqrt3 - 29sqrt3)m`
`= 58sqrt3 m`
Concept: Heights and Distances
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