Question

In the problem, $s$denotes the length of the arc of a circle of radius $r$subtended by the central angle $\theta$. Find the missing quantity. Round answers to three decimal places.

$r=2$inches, $\theta =30°$, $s=?$

Short answer

The required length s of the arc is$1.05inches.$

Step-by-step solution

Step 1. Given information

$r=2inches,\theta =30°,s=?$

Step 2. Formula Used

For a circle of radius $r$, a central angle of $\theta$radians subtends an arc whose length $s$is

$s=r\theta$

Step 3. Calculation

We have,

$r=2inchesand\theta =30°$

We know,$\theta =30°=\frac{\mathrm{\pi }}{6}$radians

Now,

The length s of the arc is

$s=r\theta$

$\Rightarrow s=2\times \frac{\mathrm{\pi }}{6}$

$\Rightarrow s\approx 1.05inches$