I need the method of these... For Q2, no matter how many times I do, I got 9.57 for VB...

1. Each edge of the uniform tetrahedron ABCD has the length 4a. The point P lies on BC such that BP=3a. Find the cosine of the angle APD.

i) show that the perpendicular distance of the corner A from the plane BCD is $\displaystyle \frac{4}{3}a\sqrt{6}$, and hence

ii) show that the angle between the line AP and the plane BCD is $\displaystyle sin^{-1}\sqrt{\frac{32}{39}}$

2. The horizontal base of a pyramid is an equilateral triangle ABC with each side 10m long. The vertex V of the pyramid is at a height of $\displaystyle \frac{10\sqrt{6}}{3}$m above the base. Find VB.

i) If the point P lies on VB such that VP=$\displaystyle \frac{1}{5}VB$, find AP.

Answer:

1. $\displaystyle \frac{5}{13}$

2. VB=10m, AP=$\displaystyle 2\sqrt{21}$m