Math Abitur: How did they arrive at these values?

Bad pattern solution.

The x1x2 plane (underground plane) is the plane which extends in the x1 or x2 direction. Therefore, the normal vector of this plane, i.e. the vector which is perpendicular to this plane, is arbitrary in the components x 1 and x 2 0 and in the component x 3 . It is intended to show exactly perpendicularly away from the plane, but no matter how long it is, it is only about the direction. Here, the vector (0 / 0 / 1) was simply selected for this normal vector.

For the use of the sine they also simply omitted the explanation: You shall calculate the angle between the ground plane and light. Since the substrate extends perpendicular to its normal vector, instead of it, you can calculate the angle between the normal vector and the light and pull it off from 90°.
In this chart you can see this (Source:

Here you can either calculate alpha directly (smooth) or beta with the direction vector of the straight lines (in your case just calculate any vector) and the normal vector of the plane (simply) and then take off from 90°.

Normally, the Arcus Cosinus (“cos^-1”) of the fracture in the formula is used for the angle calculation between vectors, but if you want to take off the angle of 90°, you can also use the Arcus Sinus (“sin^-1”) instead. (or the sine on the other side of the equation as they did here)