Chapter 4.8, Problem 24E

Solution

To find: The distance between the observer and a point on the ground directly under the balloon.

8271.02 ft

Given information:

Given, a hot-air balloon over Park City, Utah, is 760 ft above the ground. The angle of depression from the balloon to an observer is 5.25°.

Calculation:

The triangle representing the data is:

  

The angle from the point on the ground directly under the balloon to the observer is also 5.25° because they are alternate interior angles.

Using definitions of trigonometric functions for the triangle ABC:

  $\begin{array}{l}\tan A=\frac{\text{opposite side}}{\text{adjacent side}}\\ \tan 5.25°=\frac{760}{x}\\ x=\frac{760}{0.0919}\\ x\approx 8271.02\end{array}$

The distance between the observer and a point on the ground directly under the balloon is approximately 8271.02 ft.

Conclusion:

8271.02 ft