Finding the angle between a prism's edge and one of its faces.

Question

I’m having difficulty on how to start off the following question:

I know that forming a right-angled triangle AMJ with M as the midpoint of GH could be a good starting point, but I'm not sure how to proceed from there.

Any ideas on how to proceed from here would be greatly appreciated.

Answer 1

First, let's find $x$. $\triangle CDE$ is isosceles with legs $8$ and base angle $\pi \over 6$. Thus, $x=8\sin \frac{\pi}{3}=4\sqrt 3$.

Let $M$ be midpoint of $GH$. We have that $JM$ is perpendicular to the base thus $\angle JAM$ will be the required angle.

We also have that $AM^2=x^2+12^2, JM=x+\frac{x}{\sqrt 3}$. Can you finish?