Since [tex]M[/tex] is the midpoint of $AB$ , can you find the length of line segment joining midpoint of $HG$ and $M$??
that line will bisect HG and will be perpendicular to it , right?
in the plane $HMG$
the you have the length of altitude and the side opposite to it in the smaller triangle formed.
$\tan\left(\frac{\angle HMG}{2}\right)=\frac{3}{ \text{ length of altitude}}$
can you take it from here?
