Chapter 8.5, Problem 16PPS

To determine

To calculate:

The distance between worker and the truck

Answer to Problem 16PPS

The distance between worker and the truck is $20.9ft$

Explanation of Solution

Given information:

Height: $30ft$

Angle: $70°$

Calculation:

Let’s draw a figure to represent the given information:

  

If is a $△ABC$ right triangle with acute $\angle A$ , then the tangent of $\angle A$ is the ratio of the length of

leg opposite $\angle A$ to the length of the leg adjacent $\angle A$ .

As per the definition of tangent:

  $\begin{array}{l}\tan 70°=\frac{30}{x}\\ x=\frac{30}{\tan 70°}\\ x\approx 10.9ft\end{array}$

Now, the worker stands $10ft$ from the pole, so the distance between worker and the truck is:

  $\begin{array}{l}d=10.9+10\\ d=20.9ft\end{array}$