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 of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

Answer 1

Height of the balloon from the ground = 88.2 m 

Height of the girl = 1.2 m 

Angles of elevations = 60° and 30°

Let the distance travelled = dm 

From the figure 

tan 60° = \(\frac{87}{x}\)

√3 = \(\frac{87}{x}\)

⇒ 87 = √3x …….(1) 

⇒ x = \(\frac{87}{\sqrt{3}}\) m 

Also tan 30° = \(\frac{87}{x+4}\)

⇒ \(\frac{1}{\sqrt{3}}\) = \(\frac{87}{x}\)

⇒ 87 = \(\frac{x+d}{\sqrt{3}}\) ………(2) 

From equations (1) and (2)

√3x = \(\frac{x+d}{\sqrt{3}}\)

√3 × √3x = x + d 

⇒ 3x = x + d 

⇒ 2x = d