Determine the length of the radius of the circle measured in

Determine the length of the radius of the circle (measured in feet) when the angle has a measure of 166 degrees and cuts off an arc length of 42 feet.

Solution

Solution:

An angle (theta) in radians is defined as arc length (s) per radius (r),

=> angle in radians = arc/radius

=> radius = arc / angle in radians = {arc/(angle in degree * pi/180)} = {(arc * 180) / (angle in degree*pi)}

=> radius = (42*180)/(166*pi) = 14.496 ft