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).