1.12: Angles in a right pyramid

Figure 1 shows the right pyramid $\displaystyle ABCDE$. Its base $\displaystyle ABCD$ is a horizontal rectangle with $\displaystyle AD=12\,\mathrm{cm}$ and $\displaystyle CD=16\,\mathrm{cm}$. The height $\displaystyle ME$ is $\displaystyle 14\,\mathrm{cm}$, where $\displaystyle M$ is the point of intersection of the diagonals of the base. The sloping edges are all of equal length.

(a) Calculate, to 3 significant figures, the length of a sloping edge.

Calculate, in degrees to one decimal place, the size of

(b) the angle between $\displaystyle AE$ and the base,

(c) the angle between the plane $\displaystyle AED$ and the base.