coordinate geometry: circles - Calculate the arc length of a circle that has a central angle of 105 degrees and a circumference of 20. Refer to the following figure to help calculate the solution.

Krishna (last edited 3 years ago) (Expert, Educator @Qalaxia)

Step 1: Note down the given values

Step 2: Set up the formula for arc length.

NOTE: The formula is arc length (s) = \frac{\theta}{360} *C

Where, s = Arc length

C = Circumference

\theta = Central Angle

Step 3: Plug the circumference of the circle into the formula.

Step 4: Plug the value of the arc’s central angle into the formula.

Step 5: Simplify the equation to find the arc length

NOTE: Use multiplication and division to simplify the equation.

EXAMPLE: arc length (s) = \frac{\theta}{360} *C

= \frac{105}{360}*20

Arc\ lengths=5.8333