gaokao 2018 Q20

gaokao · China · national-II-science 12 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines
(12 points)
As shown in the figure, in triangular pyramid $P - A B C$, $A B = B C = 2 \sqrt { 2 }$, $P A = P B = P C = A C = 4$, $O$ is the midpoint of $A C$.
(1) Prove that $P O \perp$ plane $A B C$;
(2) Point $M$ is on edge $B C$ such that the dihedral angle $M - P A - C$ is $30 ^ { \circ }$. Find the sine of the angle between $P C$ and plane $P A M$. 
(12 points)

As shown in the figure, in triangular pyramid $P - A B C$, $A B = B C = 2 \sqrt { 2 }$, $P A = P B = P C = A C = 4$, $O$ is the midpoint of $A C$.

(1) Prove that $P O \perp$ plane $A B C$;

(2) Point $M$ is on edge $B C$ such that the dihedral angle $M - P A - C$ is $30 ^ { \circ }$. Find the sine of the angle between $P C$ and plane $P A M$.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20