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