Looking at a few more decimal places, it seems to maybe be the square root of 16.25. But so far, that's no help to me.
Twenty-five years ago, or more, I knew how to manually calculate a bearing-bearing intersection. Assigning the intersection of the provided lines the coordinates (2,0), the midpoint of one hypotenuse is (1,-1.5) and the other at (5,-1.5). Perpendiculars from those points would intersect at the radius point.
But 25 years of having a computer do the work for me hasn't done much for my memory of how to manually do it. And besides, you've probably got a more elegant solution, anyway.
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