Determine the measure of an angle in degrees that cuts off a

Determine the measure of an angle (in degrees) that cuts off an arc length of 6 inches in a circle with a 6 inch radius.

_______ degrees   

Determine the measure of an angle (in degrees) that cuts off an arc length of 18 inches in a circle with a 6 inch radius.

_______ degrees   

Determine the measure of an angle (in degrees) that cuts off an arc length of 25.8 inches in a circle with a 6 inch radius.

_______degrees

Solution

a) Arc length S = radius(R)*angle(Theta) ====> Angle = S/R = 6/6 = 1 radian = 57.3 degree

b) Arc length S = radius(R)*angle(Theta) ====> Angle = S/R = 18/6 = 3 radian = 171.9 degree

c) Arc length S = radius(R)*angle(Theta) ====> Angle = S/R = 25.8/6 = 4.3 radian = 246.4 degree