Real world Appliation (arc, cord, and radius) HELP?

[wbass77]

Hello, This is my first time visiting this site and possibly my first time asking for math help. I use to be a math wiz but it has been sooooo long since I have had to apply geometry and trig that I have forgot most of it. I had the calculus series in college for an easy elective so in response to my question, you can assume that I am not a novice.

Here is my question. On a circle, I know the arc length and the cord length and I want to solve in terms of radius. Is this possible?

This question arises from a motorcycle application. I am trying to find a fender that is similar radius as my tire, howevere the fender manufactures do not give you the radius of the fender. They are always described in terms on arc length and cord length. Any help would be greatly appreciated.

 

[wbass77]

I also know that the arc length formula, r=s/theta, but theta is unknown and not measurable.

I also realize that the radius can be measured using an isosceles triangle, however the height of the triangle is also immeasurable.
is also unmeasurable.

 

[Deleted member 4993]

I also know that the arc length formula, r=s/theta, but theta is unknown and not measurable.

I also realize that the radius can be measured using an isosceles triangle, however the height of the triangle is also immeasurable.
is also unmeasurable.

can you assume s/(2r) < 1 --- a small number?

 

[pka]

This link has what you need, I think.
http://mathworld.wolfram.com/CircularSegment.html

 

[wbass77]

I also know that the arc length formula, r=s/theta, but theta is unknown and not measurable.

I also realize that the radius can be measured using an isosceles triangle, however the height of the triangle is also immeasurable.
is also unmeasurable.

can you assume s/(2r) < 1 --- a small number?

Not sure I understand. 2r is the diameter. How can the arc length be smaller than the diameter? If the arc length = the diameter than its simply a straight line.

 

[wbass77]

This link has what you need, I think.
http://mathworld.wolfram.com/CircularSegment.html

I dont see how i can solve with out knowing the height or theta. Both of these are unknown and unmeasurable.

 

[galactus]

As in your first post, if s and c are known and you want r, then we can use the formulas

\(\displaystyle s=r{\theta}\), where \(\displaystyle {\theta}\) is the central angle.

Also, use the formula for chord length: \(\displaystyle c=2rsin(\frac{\theta}{2})\)

If we solve the first one for \(\displaystyle \theta\) and sub into the second, we get:

\(\displaystyle c=2rsin(\frac{s}{2r})\)

Solving for r may be tricky to do algebraically. But if we knew some actual units for c and s, we could use some other way such as Newton's method.

Do you have some actual values for c and s to work with?.