Trigonometry: finding the length of an arc.

150 Views Asked by At

I am currently preparing for a trig test. And I am stumped on one of the questions that involve a bicycle wheel problem. The question is

" A carbon bicycle wheel has a diameter of 700 millimeters with 16 spokes evenly distributed around the rim of the wheel. What is the length of the rim subtended by any 2 adjacent spokes."

I'm a bit dubious with my answer which is approximately 274.8.

I got this solution by taking the radius of the bicycle which is 350, and then found the circumference of the wheel with $2\pi \bullet \frac{2spokes}{16spokes} $.

after that, I used the arc length formula $ s = \theta \bullet r$ which was $ 350 \bullet \frac {\pi}{4}$ to find $s \approx 274.8$

1

There are 1 best solutions below

1
On

Between two spokes there is only one interval. So the angle is $\dfrac{2\pi}{16}$ radians.

Between $n$ spokes there are $n-1$ intervals. So the angle for this case is $\dfrac{(n-1)\pi}{16}$ radians.