Question

find the radian measure of the central angle of a circle of radius 6 yards that intercepts an arc of length 10 yards. the radian measure of the central angle is \square. (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Recall arc length formula

The formula relating arc length $s$, radius $r$, and central angle $\theta$ (in radians) is $s = r\theta$.

Step2: Rearrange to solve for $\theta$

Isolate $\theta$ by dividing both sides by $r$:
$\theta = \frac{s}{r}$

Step3: Substitute given values

Substitute $s = 10$ yards and $r = 6$ yards:
$\theta = \frac{10}{6}$

Step4: Simplify the fraction

Reduce the fraction to lowest terms:
$\theta = \frac{5}{3}$

Answer:

$\frac{5}{3}$