I am really struggling with my physics with trigonometry class.

I am really struggling with my physics with trigonometry class. Here is an problem that I simply have not been able to wrap my head around (see attachment). Would you be willing to show me step by step how to solve and why certain steps were taken? Specifically what I am wanting to understand is when to use (sin or cos). The more detailed the solution, the more it helps me. Thank you in advance!