I'm stuck. All help is greatly appreciated.
Ok since the problem stated that cos is a acute angle that means you in the 1st quad so your sin is going to be positive as well.
Now use pyth to figure out what sin A is
$\displaystyle y^2 + 1^2 = 3^2$
$\displaystyle y^2 = 8$
$\displaystyle y = 2\sqrt{2}$
so
$\displaystyle \sin {A} = \frac{2\sqrt{2}}{3}$
Now
$\displaystyle \sin{2A} = 2\sin{A}\cos{A}$
Can you finish up