As a side comment to sibling comments with various approaches, there's a handy bit of intuition/technique to this that's useful for 5th to 105th graders - when you notice 'useful' angles in a plane geometry problem, make the thing they suggest out of them. So, 60 deg angle is a piece of an equilateral triangle - finish the whole triangle and see if you get any ideas. The unit circle sin/cos thing teaches you all sorts of stuff about right-angled triangles. See a problem without a right angled triangle? Draw a line to add one, etc.