Question

A ship leaves a port R and sails on a bearing of 160 degrees to port S.
a) Draw a diagram to represent this information
b) Calculate the distance that it has traveled South.
c) Fund the distance that it traveled East.
d) What is the bearing of point R from S?

Answer 1

I think a piece of information is missing (the length RS). I’ll give the diagram instructions and the answers in terms of the distance RS = d; if you tell me d I can give numeric distances.

(a) Diagram (how to draw it)
- Draw north as up and east to the right.
- Mark point R. From R, draw the line to S making a bearing of 160° (i.e. measure 160° clockwise from north). This line points mostly south but slightly east (20° east of due south).
- Label the angle at R as 160° from the north line, and mark the 20° between the south direction and the RS line.
- Mark S at the end of that line.

(b) Distance traveled south
If RS = d, the southward component = d cos 20° ≈ 0.9397 d.

(c) Distance traveled east
Eastward component = d sin 20° ≈ 0.3420 d.

(You get these because bearing 160° is 20° east of south, so resolve d into south = d·cos20° and east = d·sin20°.)

(d) Bearing of R from S
The reverse bearing is 160° ± 180° = 340° (equivalently N 20° W).