Question

Circle O shown below has an arc of length 10 inches subtended by an angle of 0.6radians. Find the length of the radius, x, to the nearest tenth of an inch.10=0.6 rad10 inches

Answer 1

16.7 inches

Explanation:

Given:

• Length of an arc = 10 inches

,

• The angle subtended at the center = 0.6 radians

We are required to find the length of the radius.

The length of an arc, s is calculated using the formula:

`\begin{gathered} s=\theta r \\ where: \\ \theta=Central\;Angle\text{ \lparen in radians\rparen} \\ r=Radius \end{gathered}`

Substitute the given values:

`10=0.6r`

Divide both sides by 0.6:

`\begin{gathered} (10)/(0.6)=(0.6r)/(0.6) \\ r\approx16.7\text{ inches} \end{gathered}`

The length of the radius is 16.7 inches (correct to the nearest tenth of an inch).