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Question
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.
Solution
Let the initial position A of balloon change to B after some time and CD be the girl.
In ΔACE,
`("AE")/("CE") = tan 60°`
`("AF" - "EF")/("CE")` = tan 60°
`(88.2 - 1.2)/("CE") = sqrt3`
`87/("CE") = sqrt3`
`"CE" = 87/sqrt3`
`"CE"= 29sqrt3 m`
In ΔBCG,
`("BG")/("CG")` = tan 30°
`(88.2-1.2)/("CG") = 1/sqrt3`
`87sqrt3 m = "CG"`
Distance travelled by balloon = EG = CG − CE
= `(87sqrt3 - 29sqrt3)m`
= `58sqrt3 m`
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