Final answer:
To find the distance traveled by the balloon during the interval, we can use trigonometry and the given angles of elevation. Using the tangent function, we can find the distances from the girl's eyes to the balloon at different angles of elevation. The difference between these distances gives us the distance traveled by the balloon.
Step-by-step explanation:
To find the distance traveled by the balloon during the interval, we need to use trigonometry and the given angles of elevation.
When the angle of elevation is 60°, the height of the balloon is 88.2 m above the ground. We can use the tangent function to find the distance from the girl's eyes to the balloon:
tan(60°) = opposite/adjacent = 88.2/x
x = 88.2 / tan(60°) = 152.28 m
When the angle of elevation is 30°, the height of the balloon is still 88.2 m above the ground. Using the same tangent function, we can find the new distance from the girl's eyes to the balloon:
tan(30°) = 88.2/y
y = 88.2 / tan(30°) = 152.28 m / √3 = 88.2√3 m
The distance traveled by the balloon during the interval is the difference between the two distances:
Distance traveled = y - x = (88.2√3 - 152.28) m ≈ 58.1 m