Answer :
We are asked to determine the angle "x" that will produce arclength of 6 inches in a circle with a radius of 4 inches. To do that we will use the following formula:
[tex]S=r\theta[/tex]Where:
[tex]\begin{gathered} S=\text{ arclength} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]Now, we solve for the angle by dividing both sides by "r":
[tex]\frac{S}{r}=\theta[/tex]Now, we plug in the values:
[tex]\frac{6in}{4in}=\theta[/tex]Now, we solve the operations:
[tex]1.5rad=\theta[/tex]Therefore, the angle is 1.5 radians.