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**+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