Answer:
[tex] \sqrt{\frac{668}{\pi} } [/tex] feet given the area is 167 ft squared
Step-by-step explanation:
Since our sector as a central angle of 90 degree then it is only a 4th of the whole circle. The area of a circle is pi*r^2. We will only be using a 4th of that since are sector is only a 4th of the circle.
So the formula will be using for the area of our sector is A=1/4 *pi*r^2.
We are given the area is 167 so replace A with 167.
167=1/4 * pi *r^2
Multiply both sides by 4.
167*4 =pi * r^2
668=pi * r^2
Divide both sides by pi
668/pi =r^2
Square root both sides
[tex] \sqrt{\frac{668}{\pi} } =r [/tex]
