Now you know the missing angle is 33 degrees you can use the sine rule:
$\displaystyle \dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}$ where side a is opposite angle A and the same for B and C
In other words $\displaystyle \dfrac{a}{\sin 33^{\circ}} = \dfrac{11}{\sin 90^{\circ}}$ and since $\displaystyle \sin 90 = 1$ then you can solve for the missing side a:
edit: the title is misleading if you want to find out the side...
Both ways are correct, I checked Dr Steve's method and got 5.99 [only put 6 if you were instructed to round to the nearest whole number].
Is your calculator in degrees mode?
Edit: if you think about it $\displaystyle |\cos(x)| \leq 1$ so the answer won't be more than 11 for sure. I'm confused as to how you get 57.98...
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