Question

The spokes of a bicycle wheel form 10 congruent central angles. The diameter of the circle formed by the outer edge of the wheel is 18 inches. What is the length, to the nearest tenth of an inch, of the outer edge of the wheel between two consecutive spokes? A. 1.8 inches B. 5.7 inches C. 11.3 inches D. 25.4 inches

Answer 1

`5.6` inches.

Explanation:

The length of the outer edge of the wheel between two consecutive spokes is given by;

`l=d\sin((\theta)/(2) )`

where d=18 inches.

and

`\theta=(360\degree)/(10)=36\degree` is the central angle.

We substitute the values to obtain;

`l=18\sin((36\degree)/(2))`

`l=18\sin(18\degree)`

`l=5.562305899`

`l=5.6` inches to the nearest tenth.