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What is the measure of the central angle of a circle with radius 60 centimeters that intercepts a 15π centimeters arc?

adore.nuk  Feb 28, 2018
 #1
avatar+12560 
+2

As Alan pointed out to me yesterday:

By definition the angle in radians is simply the arc length divided by the radius.

15pi/60  =  pi/4

 

 

Another (longer way):
Circumference = pi x d   =  pi x 2r == 120 pi for this circle

set this up as a ratio

  

       there are 2pi radians in a complete circle...

                            ..we are trying to find the fraction  that 15 pi out of 120 pi equals

15pi / 120 pi  =  ?/ 2pi      solve for ?

30pi/120 = ?   = pi/4

ElectricPavlov  Feb 28, 2018
edited by ElectricPavlov  Feb 28, 2018
 #2
avatar+588 
+1

so, my answer is looking for a degree. am i still able to enter pi/4?

adore.nuk  Feb 28, 2018
 #3
avatar+12560 
+2

pi/4   equals   45 degrees

ElectricPavlov  Feb 28, 2018
 #4
avatar+588 
+1

thank you!!

adore.nuk  Feb 28, 2018

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