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 the figure given below). Find the distance travelled by the balloon during the interval.
Height of the girl, OO’ = 1.2 m
∠AOB = 60°
∠POQ = 30°
Let OB = x m, BQ = d m, O’Q’ = y m.
AB = PQ = Q’P – Q’Q
= 88.2 – O’O = 88.2 – 1.2 = 87 m.
Let OQ = ‘y’.
Distance balloon travelled, d = BQ
= (y – x)
