Let eye of 1.2 m tall girl is A. The balloon flying 88.2 m height from ground level have angle of elevation at different distances are 60° and 30° respectively.
∴ ∠BAE = 60° and ∠DAC = 30°
BE = CD = 88.2 – 1.2 = 87 m
From right angled ∆ABE
tan 60° = BE/AB
⇒ √3 = 87/x
⇒ x = 87/√3 ……(i)
From right angled ∆ACD
tan 30° = CD/AC
⇒ 1/√3 = 87/(x + y)
⇒ x + y = 87√3
⇒ x = 87√3 – y ….(ii)
From equation (i) and (ii)
Hence, distance traveled by balloon = 58√3 m