Final answer:
The angle of descent for the airplane is approximately 14.25 degrees, calculated using the inverse tangent function applied to the right triangle formed by the altitude and the horizontal distance to the runway.
Step-by-step explanation:
To calculate the angle of descent for an airplane, we treat the problem as a right triangle where the altitude of the airplane is the vertical leg, the horizontal distance to the runway is the horizontal leg, and the line of descent is the hypotenuse.
We can use the inverse tangent function (arctan or tan-1) to find the angle of descent, which is the angle between the horizontal leg and the hypotenuse. In this problem, the altitude (vertical leg) is 15.2 miles, and the horizontal distance (horizontal leg) to the runway is 60 miles.
The angle of descent (θ) can be calculated using the formula:
θ = tan-1(altitude/horizontal distance) = tan-1(15.2 miles / 60 miles)
Now we can calculate:
θ = tan-1(0.2533)
θ ≈ 14.25°
The angle of descent is approximately 14.25 degrees.