Y in a Cube

Inside a unit cube, place a 2 dimensional letter "Y", such that each leg of the Y is the same length. Maximize the length of the legs and describe the orientation of the "Y" if
  1. The "top" two legs are at 90 degrees to each other, and 135 degrees to the third.
  2. All legs are 120 degrees from each other. [I believe this is the same as asking for the largest equilateral triangle you can inscribe in a cube.]
Source: 1. Wesley Rose. 2. Original extension.
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