Chapter 8, Problem 12CT

To determine

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

Answer to Problem 12CT

Solution:

The angle of depression from a hot-air balloon to the airport is ${1.30}^0$

Explanation of Solution

Given information:

Height of the balloon is $600$ feet and distance between Marshall Space Flight Center and airport is $5$ miles.

As $1\text{mile}=5280\text{feet}$

  $\Rightarrow 5\text{miles}=5\cdot 5280=26400\text{feet}$

That is, the balloon is flying $600$ feet directly above the Marshall Space Flight Center and the distance between this flight center and airport is $26400$ feet.

This can be represented diagrammatically as follows,

  

If two lines are parallel, then alternate interior angles are congruent.

Thus, from the figure $\angle DAC\cong \angle ACB$

Therefore,

  $\Rightarrow \tan \theta =\frac{1}{44}$

  $\Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{44}\right)$

  $\Rightarrow \theta ={1.30}^0$

Thus, the angle of depression from a hot-air balloon to the airport is ${1.30}^0$