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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°. The distance travelled by the balloon during the interval is

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29 (33 − 3) m

29 (33 + 3) m

29 (33) m

39 (33 − 3) m

answer is A.

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Detailed Solution

Given that,
Angle of elevation from the eye of the girl of the balloon at A

= 600

,
Angle of elevation from the eye of the girl of the balloon at B

= 300

,
Height of the Balloon from the ground = 88.2 m and,
Height of the girl = 1.2 m.
The situation represented diagrammatically is as follows,
Question Image

Here,
EC = AB = 88.2 – 1.2 =87m.
In

Δ E D C

tan 60 ° = E C D C ⇒ 3 = 87 D C ⇒ D C = 873 m

Now in

Δ A B D

tan 30 ° = A B B D ⇒ 13 = 87 B D ⇒ B D = 873 m

The distance travelled by balloon = BC = BD – CD.

⇒ B C = 87 3 − 13 ⇒ B C = 87 3 − 1 3 Multiply and divide by 3 . ⇒ B C = 87 33 − 3 3 ⇒ B C = 29 (33 − 3) m

Therefore, the balloon travelled

29 (33 − 3) m

during the given interval.
The correct option is 1.

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