I think we have a little communication problem here. :mrgreen:
I should have asked for a picture of what you were doing, as I'm still not sure (see below).
Below are three options:
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I read in your op that you wanted to cap the top of the rectangle with the triangle (see purple below). And my typo fix last night apparently didn't go through - sorry - as the square should have been 4.75" with the inclusion of 1/2" for seam allowance. The square would be cut in half ONCE diagonally to make two HST's. Is that what you wanted - were these for corner triangles?
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However, if you need it to be like the pink triangle, there are two options depending on where it's going.
The starting square would be 6 3/8 exactly (just as if you were making a HST).
5.5" + 7/8" = 6 3/8"
You would match up the right angles when you attached it, and the little dog ear would hang over the edge.
But ...what goes on the other side of of the pink triangle to square it off????
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OR
are you really trying to make setting triangles because your blocks are set on point? Big difference. HUGE difference.
THOSE triangles would not be HST's (cut once diagonally), but QST's (cut twice).
Then you would start with a 9 1/8" square and cut it TWICE diagonally to get 4 QST's. You might want to starch the squares before cutting them, and handle the triangles carefully as there will be 2 exposed bias edges.
Here's the calculation:
5.5" (Finished size) x 1.414 plus 1.25" = 9.027 (round up).
That way the outside edge of your quilt (or block) would not have any bias edges (which is a good thing). ;-)
Again, you would always start by matching the right angles when attaching the triangle. Don't pull on it or stretch it when placing it. And before you sew the stitch line, just open it up a bit to make sure you have the triangle going in the right direction.
Also note that all the square sizes above are exact measurements. I always like to add a little fudge room in, so I would cut them a little bit bigger.
Play with paper first if you're trying to conserve fabric - but make sure to mark the grain on the paper before cutting.