Chapter 4, Problem 97RE

Solution

To calculate: The distance of the car.

  $s=295\text{ feet}$

Given information: The angle of depression from the top of the building is the same as the angle of elevation from the car.

Let $x$ be the distance the car has travelled and let $s$

be the horizontal segment formed by the situation:

Formula used: Height and distance.

Calculation:

Using the smaller right triangle, use the tangent function to write an expression for $s$ :

  $\begin{array}{l}\tan {42}^{\circ }=\frac{150}{s}\\ s=\frac{150}{\tan {42}^{\circ }}\end{array}$

Using the larger right triangle, use the tangent function to solve for $x$:

  $\begin{array}{c}\tan {18}^{\circ }=\frac{150}{s+x}\\ s+x=\frac{150}{\tan {18}^{\circ }}\\ x=\frac{150}{\tan {18}^{\circ }}-s\end{array}$

Substitute s:

  $x=\frac{150}{\tan {18}^{\circ }}-\frac{150}{\tan {42}^{\circ }}$

Using a calculator in degree mode: $s=295\text{ft}\text{.}$