Question

find the central angle θ which subtends an arc of length 18 inches of a circle of radius 42 inches.

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 $s = 18$ inches and $r = 42$ inches:
$\theta = \frac{18}{42} = \frac{3}{7}$ radians

Answer:

$\frac{3}{7}$ radians (or approximately 0.429 radians)