Appliqué has some limitations, although in general it's a very forgiving technique. One can pretty much "draw" any shape and execute it in appliqué. Outside corners have some issues. Ninety degree corners are ok, as the inevitable fabric lumps can tuck under fairly neatly. Anything less than ninety degrees and the extra corner fabric doesn't really have any place to hide. The best bet is to replace the outside corners with inside corners.
I love me the triangle. Anything with three parts is a favorite in my book. Triangles can be spikes, sails, arrows, lots of things. They are sharp and angular in contrast to the many curves I like to use. I want to use lots of triangles, but I'd like to make them fast with nice tight corners that don't bulk up. So far, the easiest way I've figured to render a tight looking triangle is to use reverse appliqué. The triangle shape will be under the background fabric, so it recedes a bit, but that small compromise is worth it to me to avoid the bulky outside corners.
So here's how it goes:
Draw out the triangle on the foreground fabric, cut it out using some seam allowance and baste the background fabric in place.
Start sewing on a straight section. When close to the corner, make a straight cut from the edge of the seam allowance to the V of the triangle corner.
Stitch the turned fabric under to the traced corner and take a few stitches at the corner itself. There really isn't much (if any) fabric in the seam allowance at this point, but the sides will keep the seam allowance in place.
The result is a nice tight inside corner.