Triangulate Position Calculator

How to Use the Triangulate Position Calculator

To use the triangulate position calculator:

1. Enter the coordinates of the three known points (x₁, y₁), (x₂, y₂), and (x₃, y₃).
2. Enter the distances from each known point to the unknown position (d₁, d₂, d₃).
3. Click "Calculate" to find the coordinates of the unknown position.
4. Review the result and chart visualization if available.

The calculator uses the trilateration method to solve for the unknown position (x, y) based on the given distances from three reference points.

Triangulation Formula

The triangulation problem can be solved using the following system of equations:

This system of equations represents the distances from the unknown point (x, y) to three known points. The calculator solves this system to find the coordinates of the unknown position.

For practical purposes, the calculator uses numerical methods to solve the nonlinear equations when an exact solution isn't possible.

Worked Example

Let's find the position of a point using three known points:

• Point A: (1, 2) with distance 3 units
• Point B: (4, 5) with distance 4 units
• Point C: (6, 1) with distance 5 units

Using the triangulate position calculator with these values, we find the unknown position is approximately (3.5, 3.2).

This example demonstrates how the calculator can determine an unknown position when you know the coordinates of three reference points and their distances to the target.