I'm totally stumped. i know the answer won't have numbers but i'm finding it difficult to explain the solution with an alphabetical formula.

Let's call the bottom left vertex of the cube C.

AB is the diagonal distance between the opposing vertices of the cube A and B. This length is the hypotenuse of the right triangle whose legs are one edge of the cube (the line segment AC) and the diagonal on the bottom face of the cube (the line segment BC).

BC is itself a hypotenuse of a right triangle whose legs are both adjoining edges of the cube.

By the Pythagorean theorem, BC will have length that satisfies



And again by the Pythagorean theorem, AB will have length that satisfies



The angle can be written in terms of any of the six trigonometric ratios. One would be



From this ratio we can determine that .