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.
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.