1.61: Angles and Lengths in a Right Pyramid

4PM1/2/June/2019 — Question 11 · 16 marks

1.61 diagram 1
Figure 1 shows a right pyramid with vertex V\displaystyle V and square base ABCD\displaystyle ABCD, of side 16\displaystyle 16 cm.
The size of angle AVC\displaystyle AVC is 90∘\displaystyle 90^\circ.
(a) Show that the height of the pyramid is 82\displaystyle 8\sqrt2 cm.
(4)
(b) Find, in cm, the length of VA\displaystyle VA.
(3)
(c) Find, in cm, the exact length of the perpendicular from D\displaystyle D onto VA\displaystyle VA.
(3)
Find, in degrees to one decimal place, the size of
(d) the angle between the plane VAB\displaystyle VAB and the base ABCD\displaystyle ABCD,
(3)
(e) the obtuse angle between the plane VAB\displaystyle VAB and the plane VAD\displaystyle VAD.
(3)