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I can completely understand your confusion with this point. Its basically just mathematicians being their usual elegant selves. I suspect also that they thought this up later after they already had the answer to the integration. Try doing the integration in the usual way with c as the...

There was a similar problem in the 1995 3Unit HSC paper. Just the numbers changed for your problem. Lazarus' solution is correct.

For 3D trig problems, set them up like a construction on your desk using pens/pencils/rulers for the towers and buildings. On the flat page underneath your "construction", draw the North, South East West and mark in any bearings given in the question. Do this even in an exam. Don't feel...