An arc can be measured either in degree or in unit length. An arc is a portion of the circumference of the circle which is determined by the size of its corresponding central angle. We create a proportion that compares the arc to the whole circle first in degree measure and then in unit length.
(measure of central angle/360 degrees) = (arc length/circumference)
arc length = (measure of central angle/360 degrees)(circumference)
But, maybe the angle that determines the arc in your problem is not a central angle. In such a case, find the arc measure in degree, and then write the proportion to find the arc length.
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you will need to know the angle subtended by the arc; arc length = radius x angle in radians
You also need the measure of the central angle because arc length/2pi*r=measure of central angle/360.
I'm assuming that "c" is short for "circumference". The length of an arc is (circumference)*(360/angle). So the length of an arc in a circle with circumference length of 18.84 is 6782.4/angle, where the angle is measured in degrees.
To find the arc length given the radius and angle measure in degrees, you must first convert the angle from degrees to radians, using the formula: Degrees = Radians X (pi/180). Then take the radians and the radius that you are given, and put them into the formula of Q = (a/r) where Q is the angle in radians, a is the arc length, and r is the radius. When you have this, simple multiply both sides by the radius to isolate the a. Once you do this, you have your answer.
5.23