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.

$r=3$meters, $\theta =120°$, $s=?$

Short answer

The required length s of the arc is $6.28$ meters.

Step-by-step solution

Step 1. Given information

$r=3meters,\theta =120°ands=?$

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,

$r=3metersand\theta =120°=120\times \frac{\mathrm{\pi }}{180°}=2.093radians$

Now,

The length s of the arc is

$s=r\theta$

$\Rightarrow s=3\times 2.093$

$\Rightarrow s\approx 6.28$meters