Question

The two hot-air balloons in the drawing are 48.2 and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.38 above the horizontal. What is the horizontal distance x between the two balloons

Answer 1

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 $x$ 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,  $BC= 61.0-48.2 = 12.8 meter$

Now in right angle triangle ABC.....

$tan(13.38)=\frac{BC}{AC}\\ \\ tan(13.38)= \frac{12.8}{x} \\ \\ x= \frac{12.8}{tan(13.38)}=53.8$

So, the horizontal distance between the two balloons is 53.8 meters.