Answer:
The arc length is 42 in.
Step-by-step explanation:
Hint-
[tex]\text{Arc length}=r\theta\\\\\text{Sector area}=\dfrac{1}{2}\theta r^2[/tex]
when θ is radians.
Given here,
Sector area = 252 in²
Radius = 12 in
Putting the values,
[tex]\Rightarrow \text{Sector area}=\dfrac{1}{2}\theta r^2[/tex]
[tex]\Rightarrow 252=\dfrac{1}{2}\theta (12)^2[/tex]
[tex]\Rightarrow 252=\dfrac{1}{2}\theta (144)[/tex]
[tex]\Rightarrow \theta=\dfrac{252\times2}{144}[/tex]
[tex]\Rightarrow \theta=3.5\ rad[/tex]
Then the arc length will be,
[tex]\text{Arc length}=12\times 3.5=42\ in[/tex]
