A ship sails 20 km on a bearing of 248°, how far south and how far…

Step by step

The question

Question: a ship goes 20 km on a bearing of 248°: how far south and how far west is it from the start?

1 Draw the triangle

Go straight south first, then straight west: a right triangle.

The path is the long side.

In the triangle we need the angle at the start, between the path and the south line: 68°.

Careful!

The south side is next to the angle, so it uses cos.

The west side is across from it, so it uses sin.

2 How far south

cos is adjacent over hypotenuse.

So the south side is 20 times cos 68°: about 7.5 km.

3 How far west

sin is opposite over hypotenuse.

So the west side is 20 times sin 68°: about 18.5 km.

4 Check

Let's check with Pythagoras: the two legs squared add up to about 400, the path squared.

So it is right!

Let's look back.

First: draw the triangle.

Then: how far south.

Then: how far west.

Last: check.