14. 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° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.
Height of the girl is 1.2 m. The height of the balloon from the ground is 88.2 m and the angle of elevation of the balloon from the eye of the girl at any instant is () and after some time .
Let the distance travelled by the balloon from position A to position D during the interval.
AB = ED = 88.2 - 1.2 =87 m
Now, In triangle ,
In triangle ,
Thus, distance travelled by the balloon from position A to D