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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°.

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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° see figure. Find the distance travelled by the balloon during the interval.

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Let the initial position of the balloon be A and final position be B.

Height of balloon above the girl height = 88.2 m – 1.2 m

= 87 m.

Distance travelled by the balloon = DE = CE – CD

Let us redesign the given figure as per our convenient

Step 1: In right ΔBEC,

tan 30° = BE/CE

1/√3= 87/CE

CE = 87√3

Step 2:

In right ΔADC,

tan 60° = AD/CD

√3= 87/CD

CD = 87/√3

= 29√3

Step 3:

DE = CE – CD = (87√3 – 29√3)

= 29√3(3 – 1)

= 58√3

Distance travelled by the balloon = 58√3 m.

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