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 some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

Answer 1

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

In ΔACE,

`("AE")/("CE") = tan 60°`

`("AF" - "EF")/("CE")` = tan 60°

`(88.2 - 1.2)/("CE") = sqrt3`

`87/("CE") = sqrt3`

`"CE" = 87/sqrt3`

`"CE"= 29sqrt3 m`

In ΔBCG,

`("BG")/("CG")` = tan 30°

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

`87sqrt3 m = "CG"`

Distance travelled by balloon = EG = CG − CE

= `(87sqrt3 - 29sqrt3)m`

= `58sqrt3 m`