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.

Guest May 13, 2020

#1**+1 **

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

CPhill May 13, 2020