Question

Find the length $\mathit{s}$of the circular arc, the radius $\mathit{r}$of the circle, or the central angle $\theta$, as indicated.

Short answer

The Length of the arc is $\frac{\mathbf{55}\mathbf{\pi }}{\mathbf{9}}$.

Step-by-step solution

Step 1. Given information

The given radius $=5$and the central angle in radian

$\begin{array}{l}\theta ={360}^{\circ }-{140}^{\circ }\\ ={220}^{\circ }\end{array}$

Step 2. Explanation

We will use the formula of arc length,

$s=r\theta$

Step 3. Calculation

We know that,

Converting $=5$from degrees to radian

$\begin{array}{l}\theta =220.\frac{\pi }{180}\\ =\frac{11\pi }{9}\end{array}$

$\begin{array}{l}\text{Thelengthof\hspace{0.17em}the\hspace{0.17em}arc\hspace{0.17em}}s=r\theta \\ s=5.\frac{11\pi }{9}\\ =\frac{55\pi }{9}\text{\hspace{0.17em}radian}\end{array}$