A ship is due east of a harbour. Another ship is also 3km from the harbour but on a bearing 042 degrees from it

a. Find the distance between the two ships
b. Find the bearing of the second ship from the first ship

4 answers

I'm assuming your first ship is 3 km from the harbour, since you said "also 3 km" for the second ship.

Drawing a simple picture with a pencil and ruler, reasonably to scale, is very helpful for bearing questions like this one.

Draw a compass (N, S, E, W lines). At the centre, place a point labelled H to represent the harbour, because it is the point of reference.
3 cm along the East line, place a point labelled S to represent ship 1. Label line HS as 3 cm.
Construct a line from H, that is 42 degrees clockwise from the North line. 3 cm along this line, place a point labelled M to represent ship 2. Label line HM as 3 cm.

a) Draw a line between S and M so that you now have triangle HMS.
In this triangle, angle SHM can be found because it is complementary to the 42 degree angle. With this angle and the two given sides, you can use the cos law to find SM, the distance between the two ships.

b) In the same triangle, use the sin law to find angle HSM and write it on your diagram.
Now, since ship 2 is the new point of reference, draw a new compass centred at M.
If you've been using a ruler and drawing reasonably to scale, you can now look at the diagram and use your knowledge of parallel lines/angle relationships to find the angle at which line MS sits, clockwise from North, on your new compass.

a. 4.4cm
b. 048 degrees

2.5km
333°

Annabel how did you do it