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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. - Mathematics

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`

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APPEARS IN

NCERT Class 10 Maths
Chapter 9 Some Applications of Trigonometry
Exercise 9.1 | Q 14 | Page 205
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