Find the arc length of the subtending arc for an angle of 35 degrees on a circle of radius 10.

Question

Determine the arc length for the subtending arc described in each question

Answer 1

The definition of π = C/d      [where C=circumference and d=diameter]

 

    So,  C = πd = 2πr        [where r=radius]

 

The complete circumference of a circle with radius r=10 is:

           C = 2π(10) = 20π

 

Using a proportion:

     (35º/360º) = (arclength/circumference)

   So, arclength = (35/360)C = (35/360)(20π)

        arclength = 35π/18

Answer 2

To get arc length, convert 35° to radians, and multiply by the radius.

 

θ = s/r

 

s = rθ

 

θ = (35°)(π/180°) = 7π/36

 

s = (10)(7π/36) = 35π/18