# Finding the Radius when all i have is the arc length

• Dec 5th 2011, 05:11 PM
Shante
Finding the Radius when all i have is the arc length
Im not sure if Trig is the right forum to post in, I apologize if I am in the wrong spot....
I have a project at work where I was given the arc lenght of a line and was asked to find the radius of the circle. What is the formula to do this....if it exists?
Thanks
Shante
• Dec 5th 2011, 05:17 PM
skeeter
Re: Finding the Radius when all i have is the arc length
Quote:

Originally Posted by Shante
Im not sure if Trig is the right forum to post in, I apologize if I am in the wrong spot....
I have a project at work where I was given the arc lenght of a line and was asked to find the radius of the circle. What is the formula to do this....if it exists?
Thanks
Shante

$\displaystyle s = r\theta$

$\displaystyle s$ is arclength

$\displaystyle r$ is the radius

$\displaystyle \theta$ is the sector angle in radians
• Dec 5th 2011, 05:19 PM
pickslides
Re: Finding the Radius when all i have is the arc length
The radius can be found as follows

$\displaystyle r= \frac{180\times L}{\pi \times \theta}$

Where L is the arc length and $\displaystyle \theta$ is the angle corresponding to the arc length.
• Dec 5th 2011, 05:25 PM
Shante
Re: Finding the Radius when all i have is the arc length
I know i sound like a total novice here, I promise im not, its just been forever since i have even thought about this type of math.....I dont have the angle....is there a way for me to find that....all they told me is they want a 60" arc length but gave me no other information....and in order to bend the piece of metal to that arc length they need the radius....sorry!
• Dec 5th 2011, 05:35 PM
mathbyte
Re: Finding the Radius when all i have is the arc length
Hmm... you need at least two pieces of information to work with. An arc of a given length x (60" in your case) could be any radius, depending on the ange. the smaller the radius. the greater the angle.

Might you know what portion of a circle you need to bend the metal to? Half a circle? A quarter circle? A definition along those lines would give an angle and thus, allow a radius to be calculated.
• Dec 5th 2011, 06:02 PM
Shante
Re: Finding the Radius when all i have is the arc length
All they have given me at this point is the arc length, I kept trying to tell them I didnt think that was enough information. I appreciate the help

Thanks