Success with the triangle choke depends most largely on 2 important spatial relationships:
1) The relationship of your first leg to your torso
2) The relationship of your first leg to your opponent's neck / shoulders
Master these, and the second leg is fairly unnecessary (though you can add it for funsies). Your "first leg" is the one that goes on your partner's neck (the "over" leg).
So regarding relationship #1, it is vitally important that your leg be PARALLEL to your upper body, not perpendicular to it. Here's a picture that is WRONG WRONG WRONG:
Place your right leg at that angle right now. Pull your heel to your butt with all of your strength. THAT'S ALL YOU GOT? DO YOU EVEN HAMSTRING CURL, BRO?
Here's the proper relationship of your leg to your own torso:
Place your right leg into the nice, happy, position shown here, where it is parallel to your upper body. Pull your heel to your butt. FEEL THE POWER!!!!!
To say all this another way, when you connect the dots that put the "triangle" into "triangle choke", you should not be looking at the face of the triangle. Instead, you should be seeing it as a line, because the plane of the triangle is in line with your face.
For relationship #2, imagine your triangle choke as a lasso. We need to lasso the narrowest possible slice of your opponent's upper body. This is especially important if you have shorter, thicker legs, and your partner is yoked like an ox.
Many people place their legs into a triangle and the heel of the first leg winds up somewhere around their partner's armpit. Here's a picture:
This is the worst expenditure of your energy. You are literally choking their back and not their neck. Yes, if you are a gumby, you can squeeze inwards here and it doesn't matter, but for the rest of us mortals we need this to be efficient. It needs to be RIGHT.
The second group of people place their first leg so that the heel winds up at about the shoulder. Unfortunately, this is the WIDEST measurement you could create inside your lasso. It makes it very difficult to secure the second leg (if desired), and you still get a bit of collarbone/shoulder in the back of your knee.
The ideal placement of the first leg is actually so that your heel falls at or just above your opponent's far EAR. It means that instead of having your leg slightly diagonal across his shoulders, and instead of being perpendicular to his shoulder line, your feet are slightly diagonal AWAY from his body. Here's a pic:
When you place your legs like this, two great things happen: (A) You have lassoed the thinnest portion possible: his neck and his upper arm. (B) Your kneepit has nothing to chomp down upon except for the side of his neck - you will tend to find you get your hamstring right onto the neck, between the jawbone and the collarbone. It's glorious.
With these two spatial relationships in place, you can finish with one leg, with one leg and the far hand pulling down on the ankle, or with the traditional two legs. Work on whichever you prefer, or all three. But be sure you have these two things down or it'll be more work and frustration than it's worth.
Good training to you!
