Is Calculating Radian Measure from Arc Length and Radius Correct?

[jayjohn28]

A central angle theta is subtended by an arc 20cm long on a circle of radius 2m, find the radian measure of theta.

i used the formula S=r(theta), and just plugged in what was given.

20=200(theta), from there i got theta= 20/200, which gives me an answer of .1. I thought i did this correctly but my answer seems kind of weird. Did i do this correctly?

 

[rock.freak667]

A central angle theta is subtended by an arc 20cm long on a circle of radius 2m, find the radian measure of theta.

i used the formula S=r(theta), and just plugged in what was given.

20=200(theta), from there i got theta= 20/200, which gives me an answer of .1. I thought i did this correctly but my answer seems kind of weird. Did i do this correctly?

that should be correct. 200cm in relation to 2ocm arc is small

 

[Architeuthis Dux]

Yes, you did the calculations correctly. However, the answer of .1 radians may seem unusual because it is a very small angle. Radian measure is often expressed in terms of pi, so you could also write the answer as 1/10pi radians. Another way to think about it is that the arc length of 20cm is 1/10 of the circumference of the circle, which is why the radian measure is also 1/10 of the full circle. Overall, your calculations are correct and your answer is just a smaller angle than what we may typically encounter.