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

Answer:

The measure of arc is 216°

Step-by-step explanation:

Length of arc, L = 12π inches

Radius of the circle, R = 10 inches

Formula: $\theta=\dfrac{L}{R}$

Where, $\theta$ in radian.

By substituting L and R into formula.

$\theta=\dfrac{12\pi}{10}$

$\theta=\dfrac{6\pi}{5}$

Now we change radian to degree

$\text{Degree }=\dfrac{\text{Radian}}{\pi}\times 180^\circ$

$\text{Degree }=\dfrac{6\pi}{5\pi}\times 180^\circ$

Central angle = 216°

Hence, The measure of arc is 216°

Answer 2

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)