Find a side of a triangle given other two sides and an angle I have a really simple-looking question, but I have no clue how I can go about solving it?
The question is 

Find the exact value of $x$ in the following diagram:


Sorry for the silly/easy question, but I'm quite stuck! To use the cosine or sine rule, I'd need the angle opposite $x$, but I can't find that, cause I don't have anything else to help it along.
Thank You!

Call the top point $A$, the point on the bottom left $B$, and the point on the bottom right $C$. Draw the altitude from $A$ to $BC$, and call the foot of the altitude $D$. 
Now $\triangle ABD$ has angles $30^\circ$, $60^\circ$, and $90^\circ$ respectively. Therefore $BD$ has length $3$ and $AD$ has length $3\sqrt3$. Furthermore, by the Pythagorean theorem, $DC$ has length $\sqrt{7^2 - (3\sqrt3)^2} = \sqrt{22}$.
Therefore $x = BC = BD + DC = 3 + \sqrt{22}$.
(Forgive my shoddy length notation.)
