How work out the length of this side? 
This is probably so basic, but I just cannot see it.  If you do not know that the left side is $5x$ and are only given $3x$ and $4x$, how do you deduce $5x$?

As Emilio Novati implies, all right triangles, with given angle $\theta$, are "similar triangles".  So since the legs have ratio $\frac{3x}{4x}$, the hypotenuse must be a multiple of the hypotenuse with legs of length 3 and 4 which is, of course, 5.  The hypotenuse must have length 5x.
