Bearings:

Remember a bearing in mathematics is the angle in degrees measured clockwise from north. These are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.

Example:

A boat leaves the harbour and travels 9 km north west, then 12 km north. Calculate its distance and bearing from the harbour.

Answer

We need to sketch the problem first.

Since the boat travels from the harbour on a NW direction then this tells us that it is travelling at a bearing of 315°. It then travels north, which means the harbour is now at a bearing of 135° from its position now since it is now SE.

Looking at the diagram, we are asked to find an angle and a side, although the angle we have to find is outside the triangle.

Let's find the side first, which is the distance the boat is from the harbour.

We know two sides and included angle, so from the flow chart we saw previously, we know that we are using the cosine rule.

(to nearest km)

Now we can find the angle. Let's look again at the sketch.

Let's look again at the sketch.

If we find the angle labelled with a star then we can find our required angle by subtracting this answer from 180° since it is a supplementary angle (from a straight angle which adds up to 180°).

From the flow chart from before, you can see that we can use either the sine rule or the cosine rule, so let's choose the sine rule.

(to nearest degree)

Therefore the angle we require is: .

So, the boat is now 19 km on a bearing of 160° from the harbour.

	Created by Jack McKinlay about 11 years ago

SQA Maths Note on Maths - Trigonometry and Bearings, created by Jack McKinlay on 23/08/2013.