A ship sails from port X to port Y on a bearing of 075° for a distance of 60 nm.

Question

(i) How far north of port X is the ship?
(ii) How far east of port X is the ship?

Answer 1

The problem can be represented by a right triangle with hypotenuse length 60nm. The right angle we can call N in triangle NYX. XY=60. Angle NXY=75°. Distance north=XN, distance east=NY.

(i) XN=XYcos75=60cos75=15.53nm approx.

(ii) NY=XYsin75=60sin75=57.96nm approx.