As for Eagle pose, that is how it is done in Bikram, they want shoulders down, elbows down creating a stretch between the shoulder blades. Same thing for triangle, it is done that way with one leg bent.
I used to do only Bikram yoga, now I do mostly Moksha where they give you alternative ways to do different poses. I do not think there is a right or a wrong way. The pose just has to be done as it is intended, with the right alignment and the right aim.Ask them to explain the poses to you so that you get a feel for what it is they want you to aim for.