Answer
a. $r\approx 5.86$
b. $r\approx 3.03$
Work Step by Step
The area $A$ of a sector with central angle of $\theta$ radians is
$ A=\displaystyle \frac{1}{2}r^{2}\theta$.
Solving for r, multiply both sides with $\displaystyle \frac{2}{\theta}$,
$\displaystyle \frac{2A}{\theta}=r^{2}\qquad$ ... and take the square root,
$r=\sqrt{\dfrac{2A}{\theta}}$
If the angle is in degrees, convert to radians
(multiply by $\pi/180^{o}$)
a.
$ r=\sqrt{\dfrac{2\cdot 12}{0.7}}\approx$5.85540043769
$r\approx 5.86$
b.
$150^{o}=\displaystyle \frac{150\pi}{180}$ rad
$ r=\sqrt{\dfrac{2\cdot 12}{\frac{150\pi}{180}}}\approx$3.02775902642
$r\approx 3.03$
