In a regular triangular pyramid SABC, the edges BA and BC are separated by points K and L, respectively, in a 2: 1

In a regular triangular pyramid SABC, the edges BA and BC are separated by points K and L, respectively, in a 2: 1 ratio, counting from vertex B. Find the angle between the base plane ABC and the section plane SKL.

Triangles KLB and ABC are similar by a factor of 2/3. And if you draw the height from point B, it will be divided by the straight line KL with the same ratio. And since the pyramid is correct, the projection of the vertex will be at the intersection of the medians, which are divided by the intersection point by 2/1 counting from the vertex. Therefore, SKL goes through the height of the pyramid and the angle between SKL and ABC = 90 degrees.

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