Yes, they are.
No, arc measure is an ambiguous expression since it could also refer to the angular measure of the arc.
Arc measure is the number of radians. Two similar arcs could have the same arc measure. Arc length is particular to the individual arc. One must consider the radius of the arc in question then multiply the arc measure (in radians) times the radius to get the length.
The arc length is the radius times the arc degree in radians
No, in order to fine the arc length you need a formula which is: Circumference x arc measure/360 degrees
They are normally the same. However, the measure of the arc could refer to the angle subtended at the centre of the radius of curvature.
measure= same as central angle, in degrees length= like line straightened out, measured in inches, meters, feet, etc.
(arc length)/circumference=(measure of central angle)/(360 degrees) (arc length)/(2pi*4756)=(45 degrees)/(360 degrees) (arc length)/(9512pi)=45/360 (arc length)=(9512pi)/8 (arc length)=1189pi, which is approximately 3735.3536651
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.
arc length/2pi*r=measure of central angle/360
The angle measure is: 90.01 degrees
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