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.

Answer 1

Answer:

5 rad

Step-by-step 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:

$Arc\,Length=\theta\,*\,radius\\81.5\,cm = \theta\,*\,16.3\,cm\\\frac{81.5}{16.3} = \theta\\\theta=5\,rad$