Answer:
35.26 rad
Explanation:
Let's assume the cube in the figure below. If it's in the first octant, then origin (0, 0, 0) is one of the vertices and it's also the common vertex of the diagonals (OB and OE).
The point B is at the y-axis, so since the length is 8, it is (8, 0, 8), and the point E is (8, 8, 8). The vectors of the diagonals are the subtraction of the coordinates of the two points, so OB = <8, 0, 8> and OE = <8, 8, 8>. The angle between two vectors in the tridimensional space is:
θ = cos⁻¹[(OB · OE)/(|OB|·|OE|)]
The module (| |) of a vector <x, y, z> is √(x² + y² + z²)
θ = cos⁻¹[(<8, 0, 8> · <8, 8, 8>)/(√(8² + 0² + 8²) · √(8² + 8² + 8²))]
θ = cos⁻¹[(8*8 + 8*0 + 8*8)/(√128 ·√192)]
θ = cos⁻¹[128/156.77]
θ = cos⁻¹[0.8165]
θ = 35.26 rad
