Rotate that Cuboid

Geometry Level 2

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

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

Find the \(z\)-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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