Question

A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport?

Short answer

The angle of depression from the balloon to the airport is$88.7°.$

Step-by-step solution

Step 1. Given Information

The height of the hot-air balloon is $600\mathrm{feet}.$When the pilot looks down the distance of the pilot of the balloon and the flight center is $5\mathrm{miles}.$

We have to find the angle of depression from the balloon to the airport.

Step 2. Finding the angle of depression

To find the angle we will use trigonometric function tan.

First, convert $5\mathrm{miles}$to feet.

So, $5\mathrm{miles}=26400\mathrm{feet}.$

Let xbe the angle.

$$\begin{gathered} \tan x=\frac{26400}{600} \\ \tan x=44 \\ x={\tan }^{-1}\left(44\right) \\ x\approx 88.7° \end{gathered}$$

Thus, the angle of depression from the balloon to the airport is$88.7°.$