Triangulation Calculator

Triangulation

Find position using angles from two points

How to Calculate Triangulation

Step 1: Establish Baseline Distance

Measure the distance between two observation points A and B (the baseline).

Why: The baseline is the reference. Larger baselines give more accurate target positions. All angles are measured from these two points.

Step 2: Measure Angle at First Observer

From point A, measure the angle from the baseline toward the target.

Why: This angle, combined with the baseline distance, determines one side of the triangle. It anchors the target's position relative to A.

Step 3: Measure Angle at Second Observer

From point B, measure the angle from the baseline toward the same target.

Why: Two angles from different positions uniquely determine a point in 2D space. The intersection of sight lines locates the target.

Step 4: Apply Law of Sines

Use sine ratios to find distances from A and B to the target, then calculate coordinates.

Why: The Law of Sines directly relates side lengths to opposite angles. It's perfect for this triangle problem.

Step 5: Verify Results Make Sense

Check that coordinates are reasonable and distances are positive and sensible.

Why: Results should pass sanity checks. Huge or negative distances indicate calculation or input errors.

Real-World Example

Locating a Forest Fire

Scenario: Two fire watchtowers are 100 km apart. Tower A sees the fire at 45°, Tower B at 60°. Where is the fire?
Step 1: Baseline distance d = 100 km (between towers)
Step 2: Angle at A = 45° (from baseline to fire)
Step 3: Angle at B = 60° (from baseline to fire)
Step 4: Third angle C = 180 - 45 - 60 = 75°; Using Law of Sines: Distance from A = 100 × sin(60°)/sin(75°) ≈ 90 km
Step 5: Coordinates calculated; distances positive and reasonable ✓
Verification: Both distances positive; angles sum to 180°; results within expected range
Result: Fire located at approximately coordinates (x, y) relative to tower A
Interpretation: Fire crews now have precise coordinates to dispatch equipment. Triangulation enables fast, accurate location of hazards without direct measurement to the target.

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