The horizontal distance between the two balloons is 53.8 meters.
Explanation
According to the below diagram, A and B are the positions of two balloons which are 48.2 meter and 61.0 meter above the ground respectively.
Horizontal distance between two balloons is AC, which is [tex]x[/tex] meter.
A person in the left balloon observes that the right balloon is 13.38° above the horizontal. That means, ∠BAC = 13.38°
According to the diagram, [tex]BC= 61.0-48.2 = 12.8 meter[/tex]
Now in right angle triangle ABC.....
[tex]tan(13.38)=\frac{BC}{AC}\\ \\ tan(13.38)= \frac{12.8}{x} \\ \\ x= \frac{12.8}{tan(13.38)}=53.8[/tex]
So, the horizontal distance between the two balloons is 53.8 meters.
