A Lego Angle

Connect two 1x4 Lego pieces at one end, so the top piece can pivot on its connection point. Rotate it as far as possible, until the side of the top Lego piece hits the second connection button on the bottom Lego piece. What is the angle now created by the two Lego pieces?

(It's perhaps easier to understand the dimensions if you actually find some Legos to play with, but the only extra piece of information you need is this: When rotated, the corner of the top Lego piece will barely brush the side of the second connection button on the bottom Lego piece. With this, can you determine the dimensions of the connection buttons in terms of the side-length of the pieces?)

Source: Original.


Solution
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