How do I calculate arc length using the arc length equation?

[eXmag]

Homework Statement

Homework Equations

The arc length equation?

The Attempt at a Solution

I don't know where to begin.

 

[CompuChip]

What is "the arc length equation", do you mean L = r \theta (with \theta in radians)? If so, yes, that is useful. r is given, how do you find \theta?

Also in your image you have drawn a vertical line stating r = 200. That line is not a radius of the circle, did you mean to put the label next to the line OB?

 

[eXmag]

O (zero) is for origin and 200 is the radius, i just put the line there to indicate where the center of the circle is. The circle is not centered with the origin that is why, just shifted to the right.

 

[CWatters]

I would add two lines to the drawing...

1) From B to the center of the circle
2) From point B down to the x-axis.

Some triangles will be obvious.

I'd also mark the angle A-(center of circle)-B and call it θ

Then start with L = rθ and make substitutions. eg find a way to express θ in the required co-ordinates.

 

[CompuChip]

O (zero) is for origin and 200 is the radius, i just put the line there to indicate where the center of the circle is. The circle is not centered with the origin that is why, just shifted to the right.

I missed that, my bad.
Maybe it is slightly easier if you shift the center of the circle to the origin, which will make the coordinate of B (x - c, y) instead of (x, y), where (c, 0) is the center of the circle. Then, as I said, you will need to find \theta.

 

[eXmag]

Thanks so much for your help guys, i found the answer :) Regarding the L=r theta, I actually found an easier way to calculate the arc length. If u divide the theta angle in degrees by 360 and put it equal to the L divided by the circumference it gives you the exact same answer. Like this, degree/360 = L/circumference and solve for L.