Question 76
The regular triangular pyramid $SABC$ has $AB = a$, $M$ and $N$ are the midpoints of the sides $[AB]$ and $[BC]$ respectively and $SA \perp (SBC)$.
a) Find the measure of the angle of the line $SM$ with the plane $(SAN)$.
b) If $SP$ is the orthogonal projection of the segment $SM$ on the plane $(SAN)$, compute the tangent of the angle of the planes $(SPC)$ and $(ABC)$.
a) Find the measure of the angle of the line $SM$ with the plane $(SAN)$.
b) If $SP$ is the orthogonal projection of the segment $SM$ on the plane $(SAN)$, compute the tangent of the angle of the planes $(SPC)$ and $(ABC)$.