Chapter 4.8, Problem 4E

Solution

To find: The distance of the left field wall from a point on level ground directly below the top row.

360.97 ft

Given information:

Given, the top row of seats behind home plate at Cincinnati’s Great American Ball Park is 90 ft above the level of the playing field. The angle of depression to the base of the left field wall is 14º.

Calculation:

The triangle representing the data is:

  

The angle from the base of left field wall to the top row of seats is also 14° because they are alternate interior angles.

Using definitions of trigonometric functions for the triangle ABC:

  $\begin{array}{l}\tan A=\frac{\text{opposite side}}{\text{adjacent side}}\\ \tan 14°=\frac{90}{x}\\ x=\frac{90}{0.249}\\ x\approx 360.97\end{array}$

The distance of the left field wall from a point on level ground directly below the top row is approximately 360.97 ft.

Conclusion:

360.97 ft