Chapter 8.4, Problem 56PPS

To determine

The area of the practice field in square feet.

Answer to Problem 56PPS

  $210.227{\text{ft}}^2$

Explanation of Solution

Given:

The given figure is:

Calculation:

The width will be equal to:

  $\begin{array}{c}280\left(18\text{inch}\right)=5040\text{inch}\\ \text{= 420feet}\end{array}$

Let x is the length of the practice field.

According to the definition of the tangent function,

  $\begin{array}{l}\tan 40°=\frac{\text{420}}{x}\\ x=\frac{\text{420}}{\tan 40°}\\ x=\text{500}\text{.54}\end{array}$

The practice of the field will be:

  $\begin{array}{c}A=lw\\ =420\left(500.54\right)\\ =210.227{\text{ft}}^2\end{array}$