Answer:
[tex]x \approx 9.823\ ft[/tex]
Step-by-step explanation:
Remember that the area of a sector is defined as:
[tex]A = \frac{\theta}{360^\circ}\times \pi r^2[/tex]
In this problem, we are given the area [tex]A[/tex], and the angle [tex]\theta[/tex]. We can set up an equation to solve for the radius, which is x:
[tex]A = \frac{\theta}{360^\circ}\times \pi r^2\\128 = \frac{152}{360}\times \pi r^2\\128 \times \frac{360}{152} = \pi r^2\\\frac{5760}{19} = \pi r^2\\r = \sqrt{\frac{5760}{19 \pi}}\\r \approx 9.823[/tex]
