Answer
$\frac{25\pi}{24}\approx3.27$ m$^{2}$
Work Step by Step
If $\theta$ (in radians) is a central angle in a circle with radius $r$, then the area of the sector formed by angle $\theta$ can be calculated as $A=\frac{1}{2}r^{2}\theta$.
We are given that $\theta=15^{\circ}$ and $r=5$ m.
In order to convert $\theta$ to radians, we must multiply $\theta$ by $\frac{\pi}{180}$.
$\theta=15^{\circ}=15(\frac{\pi}{180})=\frac{15\pi}{180}=\frac{\pi}{12}$
Therefore, $A=\frac{1}{2}(5^{2})(\frac{\pi}{12})=\frac{1}{2}(25)(\frac{\pi}{12})=\frac{1\times25\times\pi}{2\times12}=\frac{25\pi}{24}\approx3.27$ m$^{2}$.
