A ship sails 9 km on a bearing of 130°, how far south and how far east

Step by step

The question

Question: a ship goes 9 km on a bearing of 130°: how far south and how far east is it from the start?

1 Draw the triangle

Go straight south first, then straight east: 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: 50°.

Careful!

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

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

2 How far south

cos is adjacent over hypotenuse.

So the south side is 9 times cos 50°: about 5.8 km.

3 How far east

sin is opposite over hypotenuse.

So the east side is 9 times sin 50°: about 6.9 km.

4 Check

Let's check with Pythagoras: the two legs squared add up to about 81, the path squared.

So it is right!

Let's look back.

First: draw the triangle.

Then: how far south.

Then: how far east.

Last: check.