How Does Trilateration Work?

Wikipedia defines trilateration this way:

In geometry, trilateration is defined as the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. (https://en.wikipedia.org/wiki/True_range_multilateration)

In general, trilateration requires three pieces of information: typically, two sides of a right triangle, plus the “Right” 90 degree angle. The two sides or “laterals” must be anchored to stationary surfaces in some way, such as to an airport or the fixed ground point of a satellite.

As the illustration above shows, the two sides in this instance are: 1) the distance between the satellite ground point and the airport (4,149 km), and (2) the distance between the satellite ground point and the final ping (4,879 km). A 90 degree angle at the airport completes the requirement for trilateration analysis.

How do we know the angle at the airport is 90 degrees? Because we construct it that way. Why do we construct it that way? Because a perpendicular gives us the shortest distance between the departure airport and a final ping of any radius.

An additional note. In geometry, a “Pythagorean Triple” is a triangle with one 90 degree angle opposite the hypotenuse (the only place a 90 degree angle can be in a triangle). There are many Pythagorean Triple combinations, but they all have two things in common: 1) they are all Right Triangles, and 2) all three sides of such triangles are measured with whole integers or whole integer ratios. In this particular instance, the triangle formed by the satellite, the airport, and the crash location form a 3-4-5 ratio and is therefore a Pythagorean Triple. That, in turn, assures us it is a Right Triangle.