In a regular quadrangular pyramid, the side faces are inclined to the base at an angle
| April 5, 2021 | education
In a regular quadrangular pyramid, the side faces are inclined to the base at an angle of 50 °. The angle between the opposite side faces of the pyramid is …
Since the pyramid is regular, all its side faces are isosceles triangles.
The height KH of the side face is also the median of the triangle CDK.
Vertex K of the pyramid is projected to point O, the point of intersection of the diagonals of the square ABCD.
The segment OH is the middle line of the triangle ACD, then OH is parallel to AD, and therefore perpendicular to CD.
Then OH is the projection of the KН on ABCD, and then the OНK angle = 50.
The MCН triangle is isosceles, then the MCН angle = (180 – 50 – 50) = 80.
Answer: The angle between opposite faces is 80.
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