Answer:
The exact value for the length of the arc is: [tex]\frac{11\,\pi}{4}[/tex] inches, which is approximately 8.64 inches
Step-by-step explanation:
We can solve this with proportions, knowing that the full circumference of the circle, which corresponds to an arc length of [tex]2\,\pi r[/tex], is associated with [tex]360^o[/tex]. Then we solve for the unknown arc length "x" for a subtended angle of [tex]165^o[/tex] in the proportion:
[tex]\frac{2\,\pi r}{360^o} = \frac{x}{165^o} \\\frac{2\,\pi (3)}{360^o} = \frac{x}{165^o}\\x=\frac{6\,\pi\,(165^o)}{360^o} \\x=\frac{11\,\pi}{4}[/tex]
Which is approximately 8.64 inches
