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.