Question

A jet airplane begins a steady climb of 15° and flies for two miles (measured horizontally). What is the change in altitude in feet? Round your answer to the nearest hundredth of a foot.

Answer 1

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Explanation:

To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:

tan(15°) = change in altitude / horizontal distance

We can rearrange this equation to solve for the change in altitude:

change in altitude = horizontal distance x tan(15°)

Substituting the given values, we get:

change in altitude = 2 miles x tan(15°)

We can convert the distance to feet by multiplying by 5280:

change in altitude = 2 miles x 5280 feet/mile x tan(15°)

Using a calculator, we get:

change in altitude ≈ 514.77 feet

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.