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

Oct 25, 2016

The angle of elevation is approximately ${10.72}^{\circ}$.

#### 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.

$\tan \theta = \frac{1000}{5280}$

$\theta = {10.72}^{\circ}$

Hopefully this helps!