Question

A 1.2m tall shirisha spots a balloon moving with the wind in a horizontal line at a height of 88.2m 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​

Answer 1

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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

In  right ΔBEC,

tan 30° = BE/CE

⇒ 1/√3= 87/CE

⇒ CE = 87√3 m

also,

In  right ΔADC,

tan 60° = AD/CD

⇒ √3= 87/CD

⇒ CD = 87/√3 m

 = 29√3 m

Distance travelled by the balloon =  DE = CE - CD = (87√3 - 29√3) m

= 29√3(3 - 1) m

 = 58√3 m.