In a regular triangular pyramid SABC, the edges CA and CB are separated by points K and L
In a regular triangular pyramid SABC, the edges CA and CB are separated by points K and L, respectively, in a ratio of 2: 1, counting from the vertex C. Find the angle between the base plane ABC and the section plane SKL, express the answer in degrees
By condition, CL / BL = 2/1, CK / AK = 2/1.
Let’s build the height of CH at the base of the pyramid and connect the points K and L.
Point O – the point of intersection of CH and KL.
Triangles ABC and CKL are similar in two proportional sides and the angle between them, then point O divides the height of CH in a ratio of 2/1 starting from the vertex C.
Then point O is the center of the inscribed and circumscribed circle, and the segment SO is the height of the pyramid.
Then the SKL section is perpendicular to the base plane.
Answer: The angle is 90.