Question

find the central angle θ. θ = rad

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify values of $s$ and $r$

From the figure, the arc - length $s = 7$ and the radius $r = 3$.

Step3: Solve for $\theta$

We can rewrite the formula $s = r\theta$ as $\theta=\frac{s}{r}$. Substituting $s = 7$ and $r = 3$ into the formula, we get $\theta=\frac{7}{3}$.

Answer:

$\frac{7}{3}$