Chapter 4.3, Problem 70E

To determine

Width of the river.

Answer to Problem 70E

  $\boxed{w=1.136ft.}$

Explanation of Solution

Given information: A biologist wants to know the width $w$ of a river in order to properly set instruments for studying the pollutants in the water. From point $A$ , the biologist walks downstream $\text{1}00$ feet and sights to point (see figure). From this sighting, the biologist determines that $\theta ={54}^{\circ }$ . How wide is the river?

Calculation:

Consider from the figure

Width of the river is $w$ ft.

Distance walked by biologist from $A$ to $B$ is $\text{1}00$ ft.

Angle made while sighting point $C$ from $B$ is ${54}^{\circ }$ .

  

Now, to find the width of the river

  $\begin{array}{l}\tan {54}^{\circ }=\begin{array}{c}w\\ 100\end{array}\\ 1.136=\begin{array}{c}w\\ 100\end{array}\\ w=1.136\times 100\\ w=1.136ft.\end{array}$

Hence, the width of the river is $\boxed{w=1.136ft.}$ .