Question

find the radian measure of the central angle of a circle of radius 4 yards that intercepts an arc of length 10 yards. the radian measure of the central angle is . (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Recall 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 $\theta$

We are given $s = 10$ yards and $r = 4$ yards. Rearranging the formula $s = r\theta$ for $\theta$, we get $\theta=\frac{s}{r}$.
Substitute $s = 10$ and $r = 4$ into the formula: $\theta=\frac{10}{4}$.

Step3: Simplify the fraction

$\theta=\frac{10\div2}{4\div2}=\frac{5}{2}$.

Answer:

$\frac{5}{2}$