Question

A light aircraft was traveling 171 miles per hour straight and level when the pilot measured a landmark at a 5.6 ∘ angle of depression. after 13 minutes the aircraft was directly over the landmark. at what height, to the nearest foot, is the aircraft flying?

Answer 1

The height at which the aircraft is flying is approximately 18,415 feet.

Step-by-step explanation:

To find the height at which the aircraft is flying, we need to use trigonometry. Let's start by finding the distance the aircraft travels in 13 minutes.

Since the speed of the aircraft is 171 miles per hour, we can calculate the distance using the formula

distance = speed × time

distance = 171 miles/hour × 13 minutes × (1 hour / 60 minutes) = 38.05 miles

Now, we can use the concept of the angle of depression to find the height.

The tangent of the angle of depression is equal to the height divided by the distance. Rearranging the formula, we get:

height = distance × tan(angle of depression)

height = 38.05 miles × tan(5.6 degrees)

height ≈ 3.49 miles

Converting the height to feet:

height = 3.49 miles × (5280 feet / 1 mile) ≈ 18,415 feet

Therefore, the aircraft is flying at around 18,415 feet.