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You also need the radius.

In degrees:

A full circle has 360o and a circumference of 2{pi}r. If you know the arc length, you can work out the fraction of the circumference this represents (divide arc_length by 2{pi}r) and multiply this by 360o to get the angle in degrees.

In radians:

A full circle has 2{pi} radians; using radians arc_length = angle x radius. So given an arc_length, divide by the radius to get the angle in radians.

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Q: How do you find central angle when an arc length is given?
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Related questions

How can you find the length of arc when central angle is not given?

The answer will depend on what other information is given.


How do you find the central angle of a circle if I am given the arc length and radius?

(arc length / (radius * 2 * pi)) * 360 = angle


How do you find the radius when the arc length IS GIVEN?

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How do you find the arc length when the central angle is given?

Well, in degrees, the arc is congruent to its central angle. If the radius is given, however, just find the circumference of the circle (C=πd). Then, take the measure of the central angle, and divide that by 360 degrees. Multiply the circumference by the dividend, and you will get the arc length. This works because it is a proportion. Circumference:Arc length::Total degrees in triangle:Arc's central angle. Hope that helped. :D


How do you find the arc length with the angle given?

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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If the central angle is 70 and the radius is 8cm, how do you find out the chord lenght?


How do you find arc length when given radius and chord?

You can use the cosine rule and the three lengths of the triangle to find the central angle X, (in radians). Then the length of the arc is r*X units.


How do you find the length of the arc of a circle with only the measurement of the central angle and the Circumference?

The entire circumference has a central angle of 360 degrees. The arc is a fraction of the circumference. The fraction is (central angle) divided by (360). So the arc length is: (circumference) x (central angle) / (360) .


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How do you find the length of a sector?

The answer depends on what information you do have: radius, arc length, central angle etc.