Question:

A 1.2m tall girl 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.

In ΔACE,
AE/CE = tan60°
(88.2 - 1.2)/CE = √3
CE = 87/√3
CE = 29√3

In ΔBCD,
BG/CG = tan30°
(88.2 - 1.2)/CG = 1/√3
CG = 87√3 m

Balloon travelled distance = EG = GC - EC = 87√3 - 29√3 = 58√3 m