Tri-Concave Enneagon in a Tetragon
A tri-concave enneagon of width "Y" and height "Y" with 3 legs of unit thickness "X" rest on the two lower legs +/- 135 degrees with the vertical upper leg. The centroid of the polygon is coincident at the exterior 90 degree apex of the polygon. What proportion of height "Y" is the vertical distance to the apex?
Provide your answer to 3 decimal places.