Question

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 f 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 fig.). Find the distance traveled by the balloon during the interval.

Answer 1

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