Major props to anyone who can solve this

[MRichards]

Perhaps these similar triangles are what you're after - simpler and provable without a calculator, though I still used a fair bit of working to prove the side ratios (omitted, tell me if you really want to see it).

There is also a very nice method of dividing the triangle into 3 similar regular trapezoids, but it also gets ugly at the end.

I suspect there might be a further little trick involved to reduce the working - the kind that gets mathematicians all wet around the cosines... Frankly, I still quite like my first sledgehammer approach.



perkeyone: I use Microsoft Visio for the drawings