Rotate that Cuboid

Geometry Level 2

A cuboid has base dimensions 30×20 30 \times 20 and a height of 10 10 and is lying flat on the xyxy-plane.

It undergoes two rotations—the first is 30 30^{\circ} about the edge measuring 20 20 , and the second is also 30 30^{\circ} about the edge measuring 30 30. Both rotations are such that the center of the cuboid is raised upward.

Find the zz-coordinate (that is, the altitude) of the highest point of the cuboid after applying the two rotations (to 2 decimal places).

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