An arc has a length of 25 in. The radius of the circle is 8 in. What is the degree measure of the arc?

1 Answer
Apr 29, 2018

#179# degrees

Explanation:

Arc length is given by the equation:

#l=2pir*c/360#

  • #c# is the central angle of the circle

  • #r# is the radius of the circle

And so, we got:

#25 \ "in"=2*pi*8 \ "in"*c/360#

#25 \ "in"=16pi \ "in"*c/360#

#c/360=(25color(red)cancelcolor(black)"in")/(16picolor(red)cancelcolor(black)"in")#

#c=360*25/(16pi)#

#~~179^@#

So, the central angle is #179^@#, and so the arc will have a degree measure of #179# degrees.