Question

find the radian measure of the central angle of a circle of radius 2 yards that intercepts an arc of length 6 yards.
the radian measure of the central angle is
(type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc $s$ of a circle with radius $r$ and central angle $\theta$ (in radians) is $s = r\theta$.

Step2: Solve for the central - angle $\theta$

We are given that $s = 6$ yards and $r = 2$ yards. Rearranging the formula $s = r\theta$ for $\theta$, we get $\theta=\frac{s}{r}$.
Substitute $s = 6$ and $r = 2$ into the formula: $\theta=\frac{6}{2}$.

Step3: Simplify the fraction

$\frac{6}{2}=3$.

Answer:

$3$