Help with part C) Find <HMG, can't seem to get the correct answer.

Since 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?