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A curve in the plane can be measured by connecting a finite number of points on the curve using line segments to create a polygonal path. Since it is straightforward to calculate the length of each linear segment (using Pythagorean Theorem for example), the total length of the approximation can be found by summing the lengths of each linear segment.

If the curve is not already a polygonal path, better approximations to the curve can be obtained by following the shape of the curve increasingly more closely. The approach is to use an increasingly larger number of segments of smaller lengths. The lengths of the successive approximations do not decrease and will eventually keep increasing---possibly indefinitely, but for smooth curves this will tend to a limit as the lengths of the segments get arbitrarily small.

For some curves there is a smallest number L that is an upper bound on the length of any polygonal approximation. If such a number exists, then the curve is said to be rectifiable and the curve is defined to have arc length L.

For a circular arc the angle distended (in radians) times the radius is the length of the arc.

Q: How do you measure arc length?

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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.

No, in order to fine the arc length you need a formula which is: Circumference x arc measure/360 degrees

arc length/2pi*r=measure of central angle/360

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The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.

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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.

No, in order to fine the arc length you need a formula which is: Circumference x arc measure/360 degrees

The arc length is the radius times the arc degree in radians

Yes, they are.

No, arc measure is an ambiguous expression since it could also refer to the angular measure of the arc.

No, arc measure is an ambiguous expression since it could also refer to the angular measure of the arc.

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

(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

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You also need the measure of the central angle because arc length/2pi*r=measure of central angle/360.

measure= same as central angle, in degrees length= like line straightened out, measured in inches, meters, feet, etc.