1.85: 3D angles in a pyramid

Figure 3 shows the right pyramid $ABCDE$. The base of the pyramid, $ABCD$, is a rectangle with $CD=16x\text{ cm}$ and $AD=12x\text{ cm}$. The diagonals of the base intersect at the point $X$. The edges $EA,EB,EC$ and $ED$ are all of equal length. The size of the angle between $EA$ and the base $ABCD$ is $45^\circ$.

Find, in terms of $x$,

(a) the height, $EX$, of the pyramid, (3)

(b) the length of $EA$. (2)

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

(c) the acute angle between the planes $AEB$ and $ABCD$, (3)

(d) the acute angle between the planes $BED$ and $AEC$. (3)

The area of triangle $AED$ is $250\text{ cm}^2$.

(e) Find, to 4 significant figures, the value of $x$. (3)