For me, the SOH, CAH, TOA mnemonic has been sufficient to remember my sin, cos, and tan relations long-term.

But, it is infrequent enough that I do trig problems like this that I have to work a bit to remember how to use all the equations. And, it never hurts to write my mnemonic down as I'm pulling out the equations.

I am still struggling a bit on whether or not one could have solved this "puzzle" without using the sin/cos/tan trig functions, or perhaps using them only superficially.

As far as math stuff. I do wonder about future generations. There is so much that one can look up online. I missed the slide-rules, and did very little table lookup and interpolation, but landed early in the calculator generation.

We didn't have fancy graphing calculators, or calculators that could symbolically solve/simplify equations. So, one learned things like a quadratic makes a U, a 3^{rd} order makes a sideways S, a 4^{th }order makes a W, etc.

Does having a calculator do it all for you make it easier, or harder? I suppose half of the battle would be learning how to use the calculator.