Question

Find the measure of a central angle that intercepts an arc of 81.5 cm in a circle whose radius is 16.3 cm.

5 rad
16 rad
65 rad

Answer 1

5 rad

Explanation:

Recall that the length of an arc of circumference is given by the formula:

`Arc\,Length=\theta\,*\,radius`, where
`\theta` is the subtended angle [in radians] from the circumference's center.

Therefore in this case, you know the arc length (81.5 cm), and the radius (16.3 cm), and can solve for the angle
`\theta` using the above equation as shown below:

`Arc\,Length=\theta\,*\,radius\\81.5\,cm = \theta\,*\,16.3\,cm\\(81.5)/(16.3) = \theta\\\theta=5\,rad`