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The plane section ABCD shown in the figure is cut from a cube of edge a. Find the angle which the section ABCD makes with the lower base of the cube if D and C are each at the midpoint of an edge.
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| Photo by Math Principles in Everyday Life |
Solution:
To understand more the problem, it is better to label further the given figure as follows
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| Photo by Math Principles in Everyday Life |
Since the edges of a cutting plane which are AB and CD are parallel to the four parallel sides of a cube, then two triangles formed by a cutting plane with a cube are congruent.
Since the edges of a cube are perpendicular to each other, then two triangles are right triangles.
Therefore, the angle of a cutting plane with respect to the lower base of a cube is
