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

$3.464 \text{ ft}$
$\because A = \dfrac{1}{2}r^2 \theta$ where $r$: Radius of the circle $\theta$: Central angle that subtends the arc (in radians) $A$: Area of the sector of the circle formed by the central angle $\theta$ Derive the formula for $r$: \begin{align*} A&=\frac{1}{2}r^2\theta\\\\ 2A&=r^2\theta\\\\ \dfrac{2A}{\theta}&=r^2\\\\ \pm\sqrt{\dfrac{2A}{\theta}}&=r\\ \end{align*} Since $r$ is a length, it has to be non-negative. So, $r= \sqrt{\dfrac{2 A}{\theta}}$ Using this formula gives: $r = \sqrt{\dfrac{2 \times 2}{\frac{1}{3}}} \approx \boxed{3.464 \text{ ft}}$