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.
+128460 The angle formed by the top left of the figure and shorter red line can be found as
arctan (1/2)
Similarly, the angle formed by the top of the figure and the longer red line can be found as
arctan (1/3)
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
