Upon the start of the spring semester, I've started Pre-Cal with the same task for two years now. That tasks summarize most of what you can do with right triangle trigonometry. I give the kids several triangles that fit one of two types:
You either find one angle and two sides or two angles and one side. Why is this tricky? Because at some point the student has to make choices, choices with no consequences, but a choice. Students don't like making choices and will beg for guidance. Years of believing in one true answer will do that to you I guess.
Where I help ease their fear about choices is the breakdown of these triangles. First, we discuss what would be simplest. That's never hard. Eventually they'll spot that a 3rd angle given 2 is no problem, similar with finding a 3rd side when given 2.
It's the middle that brings the challenge. At this point I start saying "it does not matter" a lot to assure them that we won't break anything. Of the two remaining items, which would like you find first?
Fun side fact: given a choice between "x" and "y" or "a" and "b" depending (even "alpha" "theta" and "phi"), 99% of the time they pick the first one: "x" and "a." That's some known stats bias, right?
Once you pick a quantity, you choose some known information to use, again it doesn't matter. At this point sin/cos/tan get reintroduced and one of them spits out our value. While practicing on their own, no one has issues with the layup value. But in the middle it can be a sea of "how do I know whether to use sin/cos/tan?" not realizing it's really up to them what to use. Or rather, the choices they make dictate the function, not the other way around.
it is a strange hurdle to overcome for the student, and for me. I can't decide if they tense up out of fear or because they haven't spent enough time in front of the material. I never hesitate to help anyone, so I hope its not fear. In some cases I've only been their math teacher for 3 months (or 12 months if they had me for Alg II). Lack of mastery we can work on, fear of failure might be the tougher enemy. It would help if I knew who I was fighting.