Going through a medium?

Geometry Level 3

Given a rectangle $$ABCD$$ such that $$BC=1 \text{ cm}. \angle AMx=45^\circ, \angle BMN=60^\circ, Mx\parallel Ny$$.

Find the perpendicular distance between lines $$Mx$$ and $$Ny$$.

Give your answer to 1 decimal place.

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