Question

Find the arc-length of a circle with the given radius r and central angle 0. Give the answer in the given unit of measure, rounded to the nearest hundredth.r = 26 km: 0 = 30

Answer 1

13.61 km

Step-by-step explanation

the length of an arc is given by:

`\begin{gathered} arc\text{ length=}(\theta)/(360)\cdot2\pi r \\ \text{where } \\ \theta\text{ is the angle} \\ r\text{ is the radius} \end{gathered}`

Step 1

let

`\begin{gathered} \theta=30\text{ \degree} \\ r=\text{ 26 }km \end{gathered}`

now, replace in the formula

`\begin{gathered} arc\text{ length=}(\theta)/(360)\cdot2\pi r \\ arc\text{ length=}(30)/(360)\cdot2\pi(26)km \\ arc\text{ length=}(30)/(360)\cdot2\pi(26)km \\ arc\text{ length=}(1560\pi)/(360)km \\ arc\text{ length=}(1560\pi)/(360)km \\ arc\text{ length=13.61 }km \end{gathered}`

therefore, the answer is

13.61 km

I hope this helps you