Answer
$\frac{8}{9}\text{ radians} \approx 0.89\text{ radians}$
Work Step by Step
We have:
radius $r=15\text{ yards}$
area = $100 \text{ square yards}$
The formula for the area of a sector is given by the formula $A=\frac{1}{2}r^{2}\theta$ where $\theta$ is the central angle in radians and $r$ is the radius. Use this formula to obtain:
$\frac{1}{2}\times(15)^{2}\times\theta=100$
$\frac{225}{2}\times\theta=100$
$\theta=100 \times \frac{2}{225}$
$\theta=\frac{8}{9}\text{ radians}\approx 0.89\text{ radians}$
