AVI310102
Bearing FROM and TO
The Reverse Bearing Problem
A controller says: "The bearing of the aircraft from the airport is 100°." This means if you stand at the airport and look toward the aircraft, you face 100° (slightly south of east).
But what if the pilot wants to fly back to the airport? The pilot needs the bearing of the airport from the aircraft — the reverse direction.
Bearing FROM and TO
The bearing of A from B means: stand at B, face North, turn clockwise until you face A.
The bearing of A from B is not the same as the bearing of B from A. They point in opposite directions.
Common Mistake
Students often confuse "bearing of A from B" with "bearing of B from A". Always ask: where am I standing? That's the point you measure FROM.
The Compass Cross Method
To find the reverse bearing, draw a compass cross (N–S–E–W lines) at both positions. Because all North lines are parallel, you can use the geometry of parallel lines to find the return bearing.
Why Does This Work?
All North lines across the Earth point toward the North Pole. The North line at the airport is parallel to the North line at the aircraft. The bearing line connecting the two points is a transversal cutting these parallel lines.
The co-interior angles (same-side interior angles) formed by a transversal cutting parallel lines add up to 180°. This is the geometric reason why the return bearing always differs by 180° from the forward bearing.
Worked Demonstration
The bearing of an aircraft from the airport is 100°. Find the bearing of the airport from the aircraft.
Step 1: Draw both positions with compass crosses.
Step 2: At the aircraft, draw the bearing line back toward the airport. Measure the angle clockwise from North.
Step 3: The bearing of the airport from the aircraft is 280°.
Notice: 280° = 100° + 180°. This is not a coincidence — it is a consequence of the co-interior angles formed by parallel North lines.
Always Draw the Compass Cross
Always draw the compass cross at both positions. Do not try to guess the return bearing mentally — draw it, measure from North clockwise, and verify. The +180° shortcut will be formalised in the next concept (Reciprocal Bearings).
Practice: Bearing FROM the Aircraft
Now practise using the compass cross method. You are given the bearing of the aircraft from the airport. Find the bearing of the airport from the aircraft.
Draw the compass cross at the aircraft's position. The North line there is parallel to the airport's North line. Measure clockwise from North to find the bearing.
Back Bearing \u2014 Tap to Place
Place the plane by tapping, then find the back bearing (plane \u2192 airport).
Exercise: Bearing FROM the Aircraft
An aircraft is on a bearing from the airport. Find the bearing of the airport from the aircraft using the compass cross method.
Random bearings — auto-next on answer.
Exercise: Calculate the Bearing
You are given the bearing of an aircraft from an airport. Calculate the bearing of the airport from the aircraft.
Numeric practice is available in the Mental Maths app.