arc length/2pi*r=measure of central angle/360
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2*pi*r/Arc length = 360/Degreesince both are a ratio of the whole circle to the arc.Simplifying,r = 360*Arc Length/(2*pi*Degree) = 180*Arc Length/(pi*Degree)
The length of an arc is the radius times the angle in radians that the arc subtends length = radius times angle in degrees times pi/180
You can think of an arc as a fraction of the circumferance of a circle. Also, a complete circle is 2pi radians, so any central angle is THETA / 2pi of a complete circle. Multiply by the circumferance to get the length of the arc: THETA / 2pi * 2(pi)(r) = THETA * r or the length of the arc is simply the radius times the central angle in radians
2*pi*r
arc length/circumference = central angle/2*pi (radians) So, central angle = 2*pi*arc length/circumference = 4.54 radians. Or, since 2*pi radians = 360 degrees, central angle = 360*arc length/circumference = 260.0 degrees, approx.