Chapter 8.7, Problem 54SPR

To determine

To calculate:

The horizontal distance between Adelina and the soccer field:

Answer to Problem 54SPR

The horizontal distance is about $376.4$ ft.

Explanation of Solution

Given information:

Vertical distance: $80ft$

Angle of depression: ${12}^{\circ }$

Calculation:

Let

  $x$: Horizontal distance

In this figure, show all information:

  

If $\Delta ABC$ is right with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of length leg opposite $\angle A$ to the length of leg adjacent $\angle A$:

By using the definition of tangent:

  $\tan {12}^{\circ }=\frac{80}{x}\mathrm{...}\left(1\right)$

By using property of multiplication:

  $\begin{array}{l}x=\frac{80}{\tan {12}^{\circ }}\\ x\approx 376.4\end{array}$

Hence, the horizontal distance is about $376.4$ ft.