I don't understand what does 'the best viewing angle' mean.

Let the billboard ends are at points A and B. Let the programmer is at point C (so, point C can move along the direct line). Then you may notice, that angle ACB is different as point C is moved. You have to find the maximal value of this angle.

P.S. I almost sure that there must be precise English term for this notion, but I do not know it. Perhaps someone helps?

'Viewing angle' is just the precise English term for this.