Question

a ship is 50 miles west and 31 miles south of a harbor what bearing should the captain use to sail directly into the harbor?

Answer 1

31.8 degrees north of east (not sure what format the question wants)

To get this answer you draw a triangle with the line between the ship and the harbor, a line going horizontally, from the ship and ending below the harbor, and a line going vertically down from the harbor to the end of the horizontal line. The horizontal line has a length of 50 and the vertical line has a length of 31. Using inverse tangent, you can find the angle between the ship and the harbor, which is

arctan(opposite/adjacent) opposite being the vertical line, and adjacent being the horizontal line

arctan(31/50) (or tan^-1(31/50))
which gets you 31.8 degrees