In a regular triangular pyramid SABC, the edges CA and CB are separated by points K and L

| August 4, 2021 | education

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.



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