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 central angle$\theta$ is $\mathbf{2}\mathbf{\text{\hspace{0.17em}radian}}$.

Step-by-step solution

Step 1. Given information

The given $\text{radius}=5$ and the length of$\text{arc}=10$

Step 2. Explanation

We will use the formula of arc length,

$s=r\theta$

Step 3. Calculation

We know that,

$\begin{array}{l}\text{Thelengthof\hspace{0.17em}the\hspace{0.17em}arc\hspace{0.17em}\hspace{0.17em}}s=r\theta \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Therefore\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\theta =\frac{s}{r}\\ =\frac{10}{5}\\ =2\text{\hspace{0.17em}\hspace{0.17em}radian}\end{array}$