Let me start with the basic geometry — Page 189, Lesson 166

I want to walk you through a really useful mental tool that pilots use in the cockpit — the 1 in 60 rule. This is a practical way to measure angles without needing a protractor, which is important because when you're flying, your hands are busy on the control yoke and the throttle, and you don't have spare hands to be measuring angles on a map with a protractor. Let me start with the basic geometry. Imagine you draw a line exactly 60 millimetres long on a piece of paper. At one end of that line, you raise a perpendicular line — that means a line going straight up at a right angle — exactly 10 millimetres high. Then you join the top of that perpendicular line to the far end of your 60-millimetre line with a sloping line called the hypotenuse. This creates a triangle, and at the corner where the 60-millimetre line meets the hypotenuse, you get an angle, which we'll call angle z. Here's the key relationship: if the adjacent side — that's the long 60-millimetre line — is 60 units long, and the opposite side — that's the perpendicular line — is 10 units long, then the angle z will be 10 degrees. If the opposite side is 5 units high, the angle z will be 5 degrees. If the opposite side is 8 units high, the angle z will be 8 degrees. This pattern holds true up to a maximum of about 20 degrees. Beyond that, the theory starts to break down, so we only use this rule for angles up to roughly 20 degrees. Now let me show you how this applies in flight. Suppose you're flying along a planned track of 100 degrees true — that's your intended path over the ground. You've flown 60 nautical miles since your last fix, and that fix was exactly on track. You now pass over a clearly recognisable ground feature — something you can positively identify on your map — and you note from your map that this feature is 4 miles to the right of your planned track. Using the 1 in 60 rule, you can establish that your actual track flown — which we call the Track Made Good, or TMG — was 4 degrees to the right of your planned track. So your TMG is 104 degrees true. You now have the information you need to calculate a correction to get back on track, and you've done it without ever pulling out a protractor to measure the angle. We'll cover how to make that correction in the next chapter. So the 1 in 60 rule is simply this: for every 60 units you travel, a 1-unit displacement off track corresponds to approximately a 1-degree angular error. In our example, 4 miles off in 60 miles gives a 4-degree error. It's a quick, practical way to assess your navigation accuracy in the air.