# 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°. Find the distance travelled by the balloon during the interval. - Mathematics

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°. Find the distance travelled by the balloon during the interval.

#### Solution

Let the initial position A of balloon change to B after some time and CD be the girl.

In ΔACE,

AE/CE = tan 60º

(AF - EF)/(CE) = tan 60º

(88.2 - 1.2)/(CE) = sqrt3

87/(CE) = sqrt3

CE = 87/sqrt3 = 29sqrt3 m

In ΔBCG,

(BG)/(CG) = tan 30º

(88.2-1.2)/(CG) = 1/sqrt3

87sqrt3 m = CG

Distance travelled by balloon = EG = CG − CE

= (87sqrt3 - 29sqrt3)m

= 58sqrt3 m

Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 10 Maths
Chapter 9 Some Applications of Trigonometry
Exercise 9.1 | Q 14 | Page 205