A 12 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 882 m from...

Question

A 12 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 882 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 see Fig 913 Find the distance travelled by the balloon during the interval

Accepted Answer

Let the initial position of the balloon be A and final position be B.

Height of balloon above the girl height = 88.2 m – 1.2 m = 87 m.

To Find: Distance travelled by the balloon = DE = CE – CD

Let us redesign the given figure as per our convenient

NCERT Solutions - Mathematics , Class 10 chapter Some Applications of Trigonometry Question 5 Solution image

Step 1: In right ΔBEC,

tan 30° = BE/CE

1/√3= 87/CE

CE = 87√3

Step 2:

In right ΔADC,

tan 60° = AD/CD

√3= 87/CD

CD = 87/√3 = 29√3

Step 3:

DE = CE – CD = (87√3 – 29√3) = 29√3(3 – 1) = 58√3

Distance travelled by the balloon = 58√3 m.

NCERT Solutions Class 10 Mathematics Solutions for Some Applications of Trigonometry - Exercise 9.1 in Chapter 9 - Some Applications of Trigonometry