When the angle is measured in radians
arc_length = angle x radius.
So,
20cm = angle x 12cm
=> angle = 20cm / 12cm
~= 1.67 radians
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Pie/2=22/7/2Angle in radians =Total length of the arc/radius of the circle
A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle, approximately 57°17'44.6"
you will need to know the angle subtended by the arc; arc length = radius x angle in radians
An arc of length 6cm subtending an angle at the centre of 1.5c is equivalent to the whole circle of length 2πr subtending 2π radians. Therefore, 6/1.5 = 2πr/2π = r : Then r = 4 cm. NOTE : A radian can be defined as the angle at the centre of a circle subtended by an arc equal in length to the radius. So an arc subtending an angle of 2 radians is twice the length of the radius. An arc subtending an angle of 1.5 radians is thus 11/2 times as long as the radius.
The relationship between the chord and the radius of the circle is Length of the chord = 2r sin(c/2) where r = radius of the circle and c = angle subtended at the center by the chord