Chapter 9.5, Problem 58SPR

To determine

To find the distance between the merry-go-round and the Ferris wheel.

Answer to Problem 58SPR

  $118.2\text{ yds}$

Explanation of Solution

Given:

The rider is at height of $80$ yards and the angels of depression are ${11}^{\circ }$ and $8^{\circ }$ respectively.

Calculation:

Drawing the diagram of the given situation as follows-

  

Now, solving for $x$ and $y$ first.

In the above triangle-

  $\begin{array}{l}\tan 11=\frac{60}{x}\\ x=\frac{60}{\tan 11}\\ x\approx 308.7\\ y=\frac{60}{\tan 8}\\ y\approx 426.9\end{array}$

Now, find the difference between $x$ and $y$ .

  $426.9-308.7=118.2\text{ yds}$

Therefore, the distance between the merry-go-round and the Ferris wheel is $118.2\text{ yds}$ .