Question

An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle elevation of the airplane's path?

Answer 1

The angle of elevation is approximately `10.72^@`.

Explanation:

We need to start by putting everything in the same units.

Let's convert `1` mile to feet.

There are `5280` feet in a mile, so we can change the initial statement to "An airplane rises vertically 1000 feet over a horizontal distance of 5280 feet".

The angle of elevation is measured by the horizontal, so the vertical rise will be opposite to the angle of elevation, `theta`, in the imaginary triangle we draw.

The proper trigonometric ratio to use will be tangent, knowing that opposite measures `1000` feet and adjacent measures `5280` feet.

`tantheta = 1000/5280`

`theta = 10.72^@`

Hopefully this helps!