Question

The length of an arc of a circle measures 0.3km. The radius of the circle measures 0.7km. What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π. Round your answer to the nearest tenth.

Answer 1

Step 1:

In this question, we are given the following:

The length of an arc of a circle measures 0.3km.

The radius of the circle measures 0.7km.

What is the degree measure of the central angle of a circle associated with this arc? Use 3.14 for Π.

Round your answer to the nearest tenth.

Step 2:

The details of the solution are as follows:

`\begin{gathered} \text{Length of an arc of a circle = 0. 3 }km \\ \text{Radius of the circle = 0. 7 }km \\ \text{Degr}ee\text{measure of the central angle of a circle = }\theta \\ \pi\text{ = 3. 14} \end{gathered}`
`\begin{gathered} \text{Length of Arc , l = }\frac{\theta}{360^0\text{ }}\text{ x 2}\pi r \\ 0.\text{ 3 = }(\theta)/(360^0)\text{ x 2 x 3. 14 x 0.7} \end{gathered}`
`\begin{gathered} 0.3\text{ = }\frac{\theta\text{ x 4.396}}{360^0} \\ \end{gathered}`

cross-multiply, we have that:

`\begin{gathered} 360\text{ x 0. 3 = 4.396}\theta \\ \text{Divide both sides by 4.396, we have that:} \end{gathered}`
`\begin{gathered} \theta\text{ = }\frac{360\text{ X 0. 3}}{4.396} \\ \end{gathered}`
`\begin{gathered} \theta=\text{ }(108)/(4.396) \\ \end{gathered}`
`\begin{gathered} \theta\text{ = 24.5677889} \\ \theta\approx24.6^{0\text{ }}(\text{ to the nearest tenth)} \end{gathered}`