1.73: 3D angles in a prism

Figure 1 shows a right prism $ABCDEFGHIJ$. The base, $DEFG$, is horizontal and is a rectangle with $DG=EF=10\text{ cm}$. The midpoint of $ED$ is $M$.

The planes $ABCDE$ and $JIHGF$ are vertical.

(a) Show that the length of $MD$ is $3\sqrt3$ cm. (2)

(b) Show that the length of $BM$, the height of the prism, is 11 cm. (2)

(c) Find, in cm to 3 significant figures, the length $BG$. (3)

Find, in degrees to 1 decimal place,

(d) the size of the angle between the planes $BCHI$ and $CHFE$, (3)

(e) the size of the angle between the planes $ABIJ$ and $BEFI$. (5)