How do you find the height of a triangle given $3$ angles and the base side? Image given. 
This question has me absolutely stumped. This is the image of the question, how can I work out $x$? I've been doing a variety of attempts but I just cant get it.

Another approach is to note that
$$
x\cot(33^\circ)+x\cot(25^\circ)=20
$$
to get
$$
\begin{align}
x
&=\frac{20}{\cot(33^\circ)+\cot(25^\circ)}\\[4pt]
&\approx5.42833368289824
\end{align}
$$
