We have the next formula in order to find the length
[tex]arc\text{ length =}\frac{2\pi r\theta}{360}[/tex]where
r=5 in
θ=270°
Then we substitute the values
[tex]\text{arc length=}\frac{2\pi(5)(270)}{360}=\frac{15}{2}\pi\text{ in}[/tex]the exact form is
[tex]\frac{15}{2}\pi\text{ in}[/tex]the approximate form is
[tex]23.56\text{ in}[/tex]