bearings in math

Welcome! I'm excited to help you master bearings today. It is a fantastic topic that bridges geometry, navigation, and trigonometry.

To make sure we pitch this at the perfect level for you, could you let me know what level of math you're currently studying, and whether you have any experience with trigonometry yet?

I'm doing GCSE/High School math and know basic trig.

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Measuring and Drawing Bearings

Calculating Bearings (Back Bearings and Geometry)

Applying Trigonometry to Bearings

Awesome! GCSE-level maths with a bit of basic trigonometry is the perfect foundation for mastering . They are actually highly visual and incredibly logical once you know the core rules.

The Core Rules of Bearings

Whenever you work with bearings, you must always follow three golden rules. No matter how complicated a geometry question looks, these rules never change:

Start from North: Your reference line is always a vertical line pointing straight up (due North).
Go Clockwise: You must always measure the angle turning clockwise from that North line.
Use Three Figures: Bearings are always written with three digits. If your angle is less than 100°, you must put a zero in front of it. For example, a 45° angle is written as 045°, and a 7° angle is written as 007°.

Let us look at a simple visualization to see how this works in practice. Imagine you are standing at point

P

and looking at another point

A

. The angle clockwise from your North line to the line

PA

is the bearing of

A

from

P

A three-figure bearing of 045 degrees measured clockwise from North.

I have started generating a diagram above to help you visualize a 045° bearing. Notice how we start at North and turn clockwise to find our direction. Before we look at how to measure or calculate these on paper, let us do a quick check to make sure the notation makes sense. If you wanted to describe a direction that is exactly East (which is a right angle of 90° clockwise from North), how would you write that as a bearing?

090°

Spot on. Writing it as 090° is exactly correct because we always use three digits to keep navigation communication completely clear.

Locating North on a Diagram

Now that you have the three rules down, let's look at how to read and sketch these in geometry problems. Whenever you encounter a bearings question, the very first thing you need to do is identify your starting point. This is the place where you are measuring from. In maths questions, pay close attention to the word from. If a question asks for "the bearing of

A

from

B

", it means you are standing at

B

. You must draw your pointing straight up at point

B

, and then measure the clockwise angle around to the line connecting to

A

A navigation diagram showing the bearing from point B to point A, with a clockwise circular angle starting from the North reference line.

I have set up a new visual placeholder to show you exactly how this looks. Notice that since we want the bearing of $A$ from $B$ , our North line lives at $B$ , and we sweep clockwise from there.

Let's test this 'from' rule. If a map shows a ship at point $S$ and a lighthouse at point $L$ , and the captain needs to calculate the bearing of the lighthouse from the ship, at which letter should you draw your North line?