Question

The two hot air balloons in the drawing are 48.2 and 66.5 m above the ground. A person in the left ballioon observes that the right balioon is 13.5° above the horizontal. What is the horizontal distance x between the two balloons?
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Answer #1

hL = height of the left balloon above the ground = 48.2 m

hR = height of the right balloon above the ground = 66.5 m

h = height of right balloon above the left ballon

h = hR - hL

h = 66.5 - 48.2

h = 18.3 m

In triangle ABC

AC = x = horizontal distance between the balloons = ?

BC = h = 18.3 m

using the trigonometric formula

tan\theta = BC/AC

tan13.5 = h/x

0.24 = 18.3/x

x = 76.25 m

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