Answer
$\color{blue}{\theta\approx 3.6 \text{ radians}}$
Work Step by Step
RECALL:
The area of a sector $(A)$ intercepted by a central angle $\theta$ on a circle whose radius is $r$ is given by the formula:
$A = \frac{1}{2}r^2\theta$, where $\theta$ is in radian measure.
Substitute the given values of the area and area of the sector to obtain:
$A=\frac{1}{2}r^2\theta
\\16=\frac{1}{2}(3.0^2)(\theta)
\\16=0.5(9)\theta
\\16=4.5\theta
\\\frac{16}{4.5}=\theta
\\3.\overline{5}=\theta
\\\color{blue}{\theta\approx 3.6 \text{ radians}}$
