My name is holly i am a tenth grader at bonita vista high school in san diego california. This is a secondary question. I am a student. What is the formoula for finding the arc length of a central angle of a circle??

Hi Holly,

If you consider a circle with radius r then its circumference is . Thus when the angle is 360o the arclength is

Arclength =

If the angle is less than 360o, that is some fraction of 360o, then the arclength is the same fraction of

Arclength =

If you measure the angle in radians rather than degrees then the expression is simpler. Since 360o is radians, the arclength in the second diagram is .


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