# Calculate the angle of elevation of the plane's flight path

## What data do we have?

After takeoff, a plane flies in a straight path for 4000 feet and gains 800 feet of altitude. What is the angle of elevation of the plane's flight path?

## Answer:

The angle of elevation of the plane's flight path is approximately 11.3 degrees.

To find the angle of elevation of the plane's flight path, we can use trigonometry. In this case, we have a right triangle formed by the plane's flight path and its gain in altitude. The altitude gained (800 feet) is the opposite side, and the distance traveled horizontally (4000 feet) is the adjacent side.

We can use the tangent function to calculate the angle of elevation: tan(θ) = opposite side/adjacent side. Substituting the values we have, we get tan(θ) = 800/4000. Solving for θ, we find that θ = arctan(800/4000).

By using a calculator, we can determine that the angle of elevation is approximately 11.3 degrees.