Classic trigonometry problem that demonstrates the spirit of the UVM Math Contest. Do you remember your angle formulas?
Difficulty: medium, if only because of the time pressure.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013
answer 11, answer 12.