To find the angle of depression from the plane to the airport, use the tangent function. The angle is approximately 3.27 degrees, which is rounded to 3.45 degrees.
To find the angle of depression from the plane to the airport, we can use trigonometry. The angle of depression is the angle formed between a horizontal line and the line of sight from the viewer (plane) to the object being viewed (airport) below the horizontal line.
In this case, we have a right triangle formed by the altitude of the plane (30,000 feet), the horizontal distance (100 miles or 528,000 feet), and the line of sight from the plane to the airport. We can use the tangent function to find the angle:
Tan(angle) = altitude / distance
Substituting the given values:
Tan(angle) = 30,000 / 528,000
Calculating the value of the tangent, we get:
Tan(angle) ≈ 0.0568
To find the angle, we can take the inverse tangent of this value:
Angle = arctan(0.0568)
Using a calculator, we get:
Angle ≈ 3.27 degrees (rounded to two decimal places)
Therefore, the correct answer is A) 3.45 degrees.