Question

if the length of an arc is 12π inches and the radius of the circle us 10 inches, what is the measure of the arc?

Answer 1

You're dealing with "arc length" here, and the formula for that is s = r*theta, where r is the radius and theta is the central angle in radians (not degrees).

Thus, s = (12pi inches) = (10 inches)(theta), so

theta = the central angle (not the measure of the arc) = (12pi)/(10 inches), or

theta = 1.2*pi (no units of measurement)

Answer 2

The measure of arc is 216°

Explanation:

Length of arc, L = 12π inches

Radius of the circle, R = 10 inches

Formula:
`\theta=(L)/(R)`

Where,
`\theta` in radian.

By substituting L and R into formula.

`\theta=(12\pi)/(10)`

`\theta=(6\pi)/(5)`

Now we change radian to degree

`\text{Degree }=\frac{\text{Radian}}{\pi}* 180^\circ`

`\text{Degree }=(6\pi)/(5\pi)* 180^\circ`

Central angle = 216°

Hence, The measure of arc is 216°