Geometry question

Question

Q. Find the radius of an arc whose central angle is 92^o and whose arc length is 168 cm. 

 

A. 168 = (92/360) × 2π(pi)r 

     168= (92/360) × 6.28r

      168 = (3,611/2,250)r

               r= 104.68

 

I just want someone to confirm that I did this correctly

Answer 1

arc length = θr

 

Where θ is the central angle in radians and r = the radius.  We have θ=92^o and arc length = 168 cm.

 

168 = (92)(r)(pi)/(180)  where (pi)/180 converts degrees into radians

 

r = (168)(180)/(92)(pi) = 104.627

 

Your conversion formula looks correct.  I used pi/180 rather than 2pi/360, but they're equivalent.  I got a slightly different answer but my calculator has a pi key so I didn't have to round it.