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 13.3° above the horizontal. What is the horizontal distance x between the two balloons?

To find the horizontal distance \( x \) between the two hot-air balloons, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.

### Step-by-Step Solution

1. **Define the variables:**
   - Height of the left balloon: \( h_1 = 48.2 \, \text{m} \)
   - Height of the right balloon: \( h_2 = 61.0 \, \text{m} \)
   - Angle of elevation from the left balloon to the right balloon: \( \theta = 13.3^\circ \)
   - Horizontal distance between the balloons: \( x \) (what we need to find).

2. **Calculate the vertical difference in height between

Learn how to calculate the horizontal distance between two hot-air balloons using trigonometry. Given the heights of the balloons and the angle of elevation observed, this problem involves applying the tangent function to find the horizontal distance. Suitable for students in Grades 10-12.

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