1.102: 3D angles in a prism

Figure 3 shows a right prism $ABCDEFGH$. The cross section $ABCD$ of the prism is a trapezium with $AB=DC$. The point $M$ lies on $AD$ and $BM$ is perpendicular to $AD$.

Given that $BM=p\sqrt q\text{ cm}$ where $q$ is a prime number,

(a) find the value of $p$ and the value of $q$. (3)

(b) Find the size of angle $BAM$ in degrees. (2)

Find, in degrees to the nearest $0.1^\circ$,

(c) the size of the angle between $EB$ and the plane $ADEH$, (4)

(d) the size of the angle between the plane $BCEH$ and the plane $ADEH$. (3)