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Question 14
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 of the balloon be A and final position be B.
Height of balloon above the girl height =88.2m1.2m=87m
Distance travelled by the balloon = DE=CECD
As per question,

In right ΔBEC,
tan 30=BECE
13=87CE
CE=873m
Also,
In right ΔADC,
tan 60=ADCD
3=87CD
CD=873m=293m
Distance travelled by the balloon =DE=CECD=(873293)m=293(31)m=583m.

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