+525 What is the measure of the central angle of a circle with radius 60 centimeters that intercepts a 15π centimeters arc?
+37153 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
