Chapter 8.2, Problem 57AYU

To determine

To find: The diameter of the wheel to the nearest foot.

Answer to Problem 57AYU

The diameter of the wheel to the nearest foot is $252\text{ft}$ .

Explanation of Solution

Given information:

The wheel had $36$ equally spaced cars each the size of a school bus and the distance between adjacent cars was approximately $22\text{feet}$ .

The angle between the centre of the wheel and the distance between the two car is calculated as,

  $\begin{array}{c}\alpha =\frac{360°}{36}\\ =10°\end{array}$

Calculate the other angle,

  $\begin{array}{l}10°+x+x=180°\\ x=85°\end{array}$

The diameter of the wheel to the nearest foot is calculated as,

  $\begin{array}{l}\frac{22}{\sin 10°}=\frac{r}{\sin 85°}\\ r=126.21\text{ft}\\ \text{2}r\approx 252\text{ft}\end{array}$

Therefore, the diameter of the wheel to the nearest foot is $252\text{ft}$ .