Question

find the radian measure of the central angle of a circle of radius 6 yards that intercepts an arc of length 15 yards. the radian measure of the central angle is \boxed{}. (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 $s=15$ yards and $r=6$ yards: $\theta = \frac{15}{6}$

Step4: Simplify the fraction

Reduce the fraction by dividing numerator and denominator by 3: $\theta = \frac{5}{2}$

Answer:

$\frac{5}{2}$