a boat sails from harbour H on a bearing of 90 degrees for 20 km. it then changes course to a bearing of 180 degrees for 30 km to a point p , what is the bearing of H from P

Answer 1

A bearing of 90^o is assumed to be dead east, while a bearing of 180^o is dead south.

The boat sails 20 km east then 30 km south. The distance between H and P is 36 km via Pythagorean theorem.

Let E be the 20 km distance, S the 30 km distance and Y the 36 km hypoteneuse.

When the boat changes direction from east to south it forms the right angle (90^o) of a triangle.

What is the angle theta formed between the the initial point H and point P of this triangle?

By the right-angle rules, theta = cos E/Y = cos 20/36 = cos (0.5555...) ~ 56^o

Thus the heading of the boat from point H to point P is 90+56 = 146^o