How can I firmly attach a Technic triangle to a turntable?
Have to say I'm not a big fan of the triangles you've already posted. In my opinion the half beams on the corners are too close together, causing stress on the elements.
Triangular technic designs are certainly possible, the following elements are useful: 

https://www.bricklink.com/v2/catalog/catalogitem.page?P=10288



https://www.bricklink.com/v2/catalog/catalogitem.page?P=57585