Question

The diameter of a circle is 8 centimeters. A central angle of the circle of the circle intercepts an arc of 12 centimeters. What is the radian measure of the angle?

Answer 1

If the diameter is 8, that means the radius is half that, or 4, now the arc made by the central angle is 12 units, thus 

$\bf \textit{arc's length}\\\\ s=r\theta \qquad \begin{cases} r=radius\\ \theta =angle\ in\\ \qquad radians\\ ------\\ r=4\\ s=12 \end{cases}\implies 12=4\theta \implies \cfrac{12}{4}=\theta \implies \boxed{3=\theta }$

Answer 2

Answer:

The measure of the angle is $3\ radians$

Step-by-step explanation:

we know that

The formula to calculate the arc length of a circle is equal to

$L=r\theta$

where

r is the radius of the circle

$\theta$ is the measure of the angle in radians

In this problem we have

$L=12\ cm, r=8/2=4\ cm$

substitute in the formula and solve for $\theta$

$12=4\theta$

$\theta=12/4$

$\theta=3\ radians$