Answer:
The radius is [tex]\frac{9}{\pi}[/tex] or 2.866
Step-by-step explanation:
Given
Central angle = 120
Length of arc = 6
Required
The radius
To solve this question, we'll apply the formula of length of an arc.
The length of an arc is calculated as follows;
[tex]L = \frac{theta}{360} * 2\pi r[/tex]
Where theta = central angle = 120
L = length of the arc = 6.
By substituting these values in the formula above, we have
[tex]6 = \frac{120}{360} * 2\pi r[/tex]
[tex]6 = \frac{1}{3} * 2\pi r[/tex]
Multiply both sides by 3
[tex]3 * 6 =3 * \frac{1}{3} * 2\pi r[/tex]
[tex]18 = 2\pi r[/tex]
Divide both sides by [tex]2\pi[/tex]
[tex]\frac{18}{2\pi} = \frac{2\pi r}{2\pi}[/tex]
[tex]r = \frac{18}{2\pi}[/tex]
[tex]r = \frac{9}{\pi}[/tex]
Leaving the answer in terms of [tex]\pi[/tex], the radius is calculated as [tex]\frac{9}{\pi}[/tex]
However, if we're to solve further
Taking [tex]\pi[/tex] as 3.14
[tex]r = \frac{9}{3.14}[/tex]
[tex]r = 2.866[/tex]
The radius is 2.866
