A balloon is connected to a meteorological ground station by a cable of length215 m inclined at 60 ^º to the horizontal. Determinethe height of the balloon from the ground. Assume that there isno stack in the cable.

Given:

Length of the cable, l = AC = 215 m

Angle of elevation, θ = 60°

To find: Height of the balloon from the ground, AB

Solution:

Let A be the position of the balloon and let AC be the length of the cable

In right angled Δ ABC,

sin θ = [Opposite] / [Hypotenuse]

sin 60° = AC/AB

And also the opposite side is AB and the hypotenuse side is AC

sin 60° = AB/AC

AB = AC sin 60 ^º

Here AC = 215 m

AB = 215 × (√3 /2)

= 215 × [1.732 / 2]

= 215 × 0.866 m

= 186 m

Therefore the height of the balloon from the ground is 186 m.