Calculate the Distance between Objects, Triangulation

Name: Calculate the Distance between Objects, Triangulation
Author: Jürgen Kummer

Calculating the distance between two objects from each other using the distance between them and the observer and the angle between them using triangulation. Triangulation means the measuring of distances in surveys with triangles. If the distance of two objects and the angle between is knwon, the distance between these objects can be calculated. The calculation is done using the second congruence theorem or SAS theorem for a triangle.

Example: The observer in the sketch above is 100 meters from the left tree and 180 meters from the right tree. The angle between the two imaginary straight lines from the observer to these trees is 36 degrees. Then the two trees are just over 122 meters apart.

The formula for the distance between both objects is:
c = √a² + b² - 2ab * cos( γ )
Analogous to this formula, if two lengths and the angle between them are known, one can calculate the third length, which also applies to the other two lengths. This formula is a generalized Pythagorean theorem, which applies not only to right triangles, but to all triangles. However, it is more complicated and uses the cosine. Cosine belongs to the mathematical field of trigonometry. Triangulation, on the other hand, is a term from metrology that is closely related to trigonometry.

Here you can do more extensive triangle calculations, because there are several possible ways to calculate the lengths and angles of a triangle, depending on the given values. The area can also be calculated here.

Last updated on 07/01/2025. Author: Jürgen Kummer

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Distance to the first object a:		m
Distance to the first object b:		m
Angle between both objects γ:		°
Distance between both objects c:		m