Question

What is the measure, to the nearest hundredth of a degree, of the central angle of an arc of 12.5 cm if the radius of the circle is 6 cm?

Answer 1

The formula for finding the angle of an arc given the radius, r, and the length, l, of that arc is:

\[\frac{\theta}{360} = \frac{l}{2 \pi r}\]

In this case, r = 6 and l = 12.5. If we input the given values into the formula we get:
\[\frac{\theta}{360} = \frac{12.5}{2 \pi (6)}\]\[\text{solve for} \space \theta\]