Final answer:
To calculate the distance traveled by the airplane between points AA and BB, we use the tangent function to find the horizontal distances for the given angles of elevation and subtract them to get the distance traveled. The calculation requires the known altitude of 6600 feet and rounding to the nearest foot.
Step-by-step explanation:
The problem is to find the distance an airplane traveled between two points AA and BB, where the angles of elevation changed from 18° to 37°, while maintaining a constant altitude of 6600 feet. This can be solved by using trigonometry to find the distances from Cameron to the airplane at points AA and BB and then using the difference of those distances to find the distance the plane has traveled between these two points.
To find the distance from Cameron to the airplane at AA (d1), we use the tangent function which relates the angle of elevation θ to the opposite side (altitude) and adjacent side (horizontal distance):
tan(18°) = altitude / d1
d1 = altitude / tan(18°)
d1 = 6600 feet / tan(18°)
Calculating d1 gives us the first horizontal distance from Cameron to the plane. Similarly, we can find d2 using the angle 37°:
tan(37°) = altitude / d2
d2 = altitude / tan(37°)
d2 = 6600 feet / tan(37°)
After calculating d1 and d2, the distance the plane has flown from AA to BB is found by subtracting these two distances:
Distance traveled = d2 - d1
The final answer should be rounded to the nearest foot, as requested.