1.93: $AB=BC=CA=10$ cm and $DA=DB=DC=13$ cm

Figure 2 shows a triangular pyramid $ABCD$.

$AB=BC=CA=10$ cm and $DA=DB=DC=13$ cm. The point $E$ is the midpoint of $AC$.

(a) Find the exact length of

(i) $DE$

(ii) $BE$ (4)

(b) Find, in degrees to 1 decimal place, the size of the angle between the line $BD$ and the line $DE$. (3)

(c) Find, in degrees to 1 decimal place, the size of the angle between the line $BD$ and the plane $ABC$. (3)

(d) Find, in degrees to 1 decimal place, the size of the angle between the plane $ADC$ and the plane $ABC$. (2)

(e) Find, to 3 significant figures, the volume of the pyramid $ABCD$. (3)