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).
by
Hosam Hajjir