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

Answer 1

Answer:

58√3 m.

Step-by-step explanation:

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

A/q,

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.

Answer 2

Answer:

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