Chapter 4.7, Problem 105E

(a)

To determine

To write: $\theta$ as a function of $x$ .

Answer to Problem 105E

  $\theta =\arctan \frac{x}{20}$

Explanation of Solution

Given information:

A police car with its spotlight on is parked 20 meters from a warehouse. Consider $\theta$ and $x$ as shown in the figure.

  

Calculation:

Write $\theta$ as a function of $x$

Taking the tangent of the angle, we get

  $\begin{array}{c}\tan \theta =\frac{x}{20}\\ \theta =\arctan \frac{x}{20}\end{array}$

(b)

To determine

To find $\theta$ , when $x=5$ meters, and $x=12$ meters.

Answer to Problem 105E

  $\theta =14.0°$ and $\theta =31.0°$ for $x=5$ meters, and $x=12$ meters respectively.

Explanation of Solution

Calculation:

From part (a) we know that $\theta =\arctan \frac{x}{20}$ , hence we substitute the value of $x=5$ meters, and $x=12$ meters.

When $x=5$

  $\theta =\arctan \frac{5}{20}\approx 14.0°$

When $x=12$

  $\theta =\arctan \frac{12}{20}\approx 31.0°$