Final answer:
To find the angle of depression from a plane to the airport, we convert the horizontal distance to feet, use the tangent ratio, and calculate the inverse tangent to get an angle of approximately 3.25°.
Step-by-step explanation:
The question is about finding the angle of depression from a plane to the airport as the plane descends. To find the angle of depression, we will use trigonometry. First, we must ensure all measurements are in the same units, so we convert the horizontal distance from miles to feet: 100 miles × 5280 feet/mile = 528,000 feet.
Next, we use the definition of the tangent of an angle in a right triangle, which is the ratio of the opposite side (the altitude of the plane) to the adjacent side (the horizontal distance to the airport).
The formula for the tangent of the angle of depression (θ) is:
tan(θ) = opposite / adjacent
tan(θ) = 30,000 feet / 528,000 feet
Now we calculate the angle θ by taking the inverse tangent (arctan) of the ratio:
θ = arctan(30,000 / 528,000)
We can use a calculator to find that:
θ ≈ arctan(0.05682)
θ ≈ 3.25°
Thus, the angle of depression from the plane to the airport is approximately 3.25°, when rounded to the nearest hundredth.