## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\frac{8}{9}\text{ radians} \approx 0.89\text{ radians}$
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: $\frac{1}{2}\times(15)^{2}\times\theta=100$ $\frac{225}{2}\times\theta=100$ $\theta=100 \times \frac{2}{225}$ $\theta=\frac{8}{9}\text{ radians}\approx 0.89\text{ radians}$