1.54: Past-paper question 11

Figure 4 shows a right pyramid $\displaystyle ABCDE$ with

• vertex $\displaystyle E$

• horizontal square base $\displaystyle ABCD$ of side 6cm

• $\displaystyle EA = EB = EC = ED = 12$ cm

• vertical height of $\displaystyle h$ cm

(a) Show that $\displaystyle h = 3\sqrt{14}$

(b) Find, in degrees to one decimal place, the size of the angle between $\displaystyle EB$ and the plane $\displaystyle ABCD$

The midpoint of $\displaystyle AE$ is $\displaystyle P$ and the midpoint of $\displaystyle BE$ is $\displaystyle Q$

(c) Find, to the nearest degree, the size of the obtuse angle between the plane $\displaystyle EPQ$ and the plane $\displaystyle PQCD$