Question 71
Let $ABCDEF$ be a regular hexagon with side length $a$. At point $A$, the perpendicular $AS$, with length $2a\sqrt{3}$, is erected on the hexagon's plane. The points $M, N, P, Q$, and $R$ are the projections of point $A$ onto the lines $SB, SC, SD, SE$, and $SF$, respectively.
a) Prove that the points $M, N, P, Q, R$ lie in the same plane.
b) Find the measure of the angle between the planes $(MNP)$ and $(ABC)$.
a) Prove that the points $M, N, P, Q, R$ lie in the same plane.
b) Find the measure of the angle between the planes $(MNP)$ and $(ABC)$.