The two hot-air balloons in the drawing are 48.2m and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3 degrees above the horizontal. What is the horizontal distance x between the two balloons?

The horizontal distance x between the two balloons is 54.15 m

Explanation:

The diagram described as obtained online is presented in the image attached to this solution.

Let the horizontal distance between the two balloons be x

Difference in height (vertical distance) between the two balloons = 61 - 48.2 = 12.8 m

Using trigonometric relations, it is evident that

Tan 13.3° = 12.8/x

x = 12.8/tan 13.3° = 12.8/0.2364 = 54.15 m

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