Three unit squares are joined side by side to form a 3 by 1 rectangle, and two diagonals are joined as shown above. Find the acute angle formed by the diagonals.
The angle formed by the top left of the figure and shorter red line can be found as
Similarly, the angle formed by the top of the figure and the longer red line can be found as
Using an obscure trig identity
arctan (u) + arctan (v) = arctan [ ( u + v) / (1 - uv) ]
arctan (1/2) + arctan (1/3) = arctan [ (1/2 + 1/3) / ( 1 - (1/2)(1/3) ) ] =
arctan [ (5/6) / (5/6) ] =
artan (1) = 45° = the angle we need