Triangulation

Part of Navigation Without Technology

Triangulation lets you fix your exact position on a landscape using nothing but your eyes, two known landmarks, and basic geometry. It is the same method that built every accurate map before satellites existed.

Why Triangulation Matters

When you are traveling through unfamiliar territory after a collapse, the most dangerous thing is not knowing where you are. Dead reckoning drifts. Memory fails. Terrain looks different from different angles. Triangulation anchors you to reality: it converts “I think I’m somewhere near that ridge” into “I am at the intersection of these two lines.”

You do not need instruments. You do not need paper. You need two identifiable landmarks and a way to estimate angles. With practice, you can fix your position within a few hundred meters using only your hands and eyes.

The Core Principle

Triangulation works because a point is uniquely defined by its angular relationship to two other known points. If you can see Landmark A and Landmark B, and you know where those landmarks are relative to each other, the angles you observe from your position create two lines that intersect at exactly one place: where you are standing.

In formal surveying, this requires precise instruments. In field survival, it requires sharp observation and reasonable estimates.

Two-Point Fix: The Basic Method

This is the workhorse technique. It requires two landmarks you can identify and that you can also locate on a sketch map or mental model of the area.

Prerequisites

• Two distinct, identifiable landmarks visible from your position (mountain peaks, towers, lone trees, river bends, rock formations)
• A general sense of the area’s layout (a sketch map, a remembered map, or landmarks whose relative positions you know)
• A way to estimate direction: a compass, shadow stick bearing, or known north reference

Step-by-Step Procedure

1. Select two landmarks that are well-separated in your field of view. Ideally they should be 60 to 120 degrees apart as seen from your position. If they are too close together (less than 30 degrees), the intersection angle becomes shallow and your fix is inaccurate.

2. Determine the bearing to Landmark A. Face the landmark. If you have a compass, read the bearing. If you have established north using a shadow stick or star method, estimate the angle from north clockwise to the landmark. Use your outstretched fist (approximately 10 degrees wide at arm’s length) to count off the angle.

3. Determine the bearing to Landmark B. Repeat the process for the second landmark.

4. Plot the back-bearings. On your sketch map or mental model, reverse each bearing by 180 degrees. From Landmark A on the map, draw (or imagine) a line in the direction of your back-bearing. Repeat from Landmark B.

5. The intersection of these two lines is your position.

Estimating Angles Without a Compass

Your body provides surprisingly consistent angle-measuring tools:

Body Reference	Approximate Angle at Arm’s Length
Thumb width	2 degrees
Three middle fingers together	5 degrees
Closed fist width	10 degrees
Spread hand (thumb tip to pinky tip)	20 degrees
Both fists side by side	20 degrees

To measure a bearing from north:

1. Face north (established by shadow stick, stars, or compass)
2. Extend your arm toward the landmark
3. Count fist-widths from your north reference to the landmark
4. Multiply by 10 degrees per fist

This gives bearings accurate to roughly 5-10 degrees, which is sufficient for a useful position fix in open terrain.

Working Example

You are traveling through a valley. To the northwest, you see a distinctive rocky peak. To the northeast, you see a church steeple in a ruined town. You know from a sketch map that the peak is roughly 4 km due north of the church.

1. You face north (established from your noon shadow line)
2. The rocky peak is about 3 fist-widths left of north = approximately 330 degrees (northwest)
3. The church steeple is about 4 fist-widths right of north = approximately 40 degrees (northeast)
4. Back-bearing from the peak: 330 + 180 = 150 degrees (southeast from the peak)
5. Back-bearing from the church: 40 + 180 = 220 degrees (southwest from the church)
6. You draw these lines on your sketch map. They cross approximately 2 km south-southwest of the peak and 3 km southwest of the church. That is your position.

The Three-Point Fix

If you can see three landmarks, take bearings to all three. Plot three back-bearing lines. They will form a small triangle (called a “cocked hat”) rather than meeting at a single point. Your position is inside this triangle. A smaller triangle means higher accuracy.

The Cocked Hat Rule

If the triangle formed by three back-bearings is large, one or more of your bearings is significantly off. Re-check the bearing to each landmark. The most common error is misidentifying a landmark or miscounting fist-widths.

Resection Without a Map

If you have no map at all, you can still use triangulation to build one:

1. Establish a baseline. Walk a known distance (pace-counted) between two points along a straight line. Mark both ends.

2. From each end of the baseline, take bearings to the same distant landmark.

3. The two bearings and the known baseline length form a triangle. Using basic trigonometry (or careful scale drawing on flat ground), you can calculate the distance to the landmark.

4. Repeat for other landmarks to build a network of known positions.

This is exactly how the first accurate national surveys were conducted in the 18th century. The method works with nothing more than a straight stick for bearing estimation and paced distances.

Common Errors and How to Avoid Them

Error	Cause	Fix
Lines do not intersect cleanly	Bearing estimation off by 10+ degrees	Use three landmarks; take average of repeated measurements
Fix places you in impossible terrain (inside a lake, on top of a cliff)	Landmark misidentification	Verify landmarks from multiple angles; look for unique features
Shallow intersection angle	Landmarks too close together in your field of view	Choose landmarks at least 60 degrees apart
Consistent offset in one direction	Systematic error in north reference	Re-establish north with a fresh shadow stick reading
Back-bearing math wrong	Forgot to add/subtract 180 degrees	If bearing > 180, subtract 180; if < 180, add 180

Magnetic Declination

If you are using a magnetic compass, remember that magnetic north is not true north. The difference (declination) varies by location and can be 10-20 degrees or more. If your sketch map is oriented to true north but your bearings are magnetic, every bearing will be offset by the declination angle. Either correct all bearings or orient your map to magnetic north and be consistent.

Field Practice Drill

Before your life depends on this skill, practice it:

1. Pick two landmarks visible from your yard or a park
2. Establish north with a shadow stick
3. Take fist-width bearings to both landmarks
4. Walk 500 paces in any direction
5. Take new bearings from the new position
6. Plot both fixes on a scratch map
7. Compare with known positions (use a phone GPS if available for verification)

Repeat until your fixes are consistently within 200-300 meters of your actual position. This is adequate accuracy for cross-country travel and rendezvous planning.

Key Takeaways

• Two landmarks and two bearings give you a position fix anywhere on the landscape without instruments
• Fist-width estimation provides 5-10 degree bearing accuracy, sufficient for field navigation
• Landmarks should be 60-120 degrees apart for a reliable intersection
• Three-point fixes are more reliable than two-point fixes and reveal your error margin
• Back-bearing = bearing plus or minus 180 degrees is the most common calculation error; double-check it every time
• Practice before you need it: triangulation is a perishable skill that improves dramatically with repetition