# Thread: Determine distance between beacons

1. ## Determine distance between beacons

d

2. Originally Posted by jfontein
Hello,

I have a practical problem which I can't solve (anymore). High-school and university (where I had some advanced math) is too long ago and I haven't kept up since...

• There are 2 beacons (1) and (2).
• The distance between (1) and (2) is known.
• These 2 beacons 'create' 2 'virtual' beacons (A) and (B), each at the intersections at distance x from both beacon (1) and (2).
• There are several candidates to become beacon number (3).
• For each of these candidates the distance to the existing beacon (1) and (2) is known.
• The ‘system’ doesn’t know coordinates.
• To determine which candidate gets priority, there are some rules related to the distance between the candidate and beacon (A) and (B).

• HOW can the distance to beacon (A) and (B) be calculated (easily) or HOW can this be (easily) approximated?
• The calculation should be simple/easy as the calculation should be performed realtime/online: at the moment a candidate shows up, it should get feed back about its priority ranking within a few seconds.

If I interpret your drawing correctly the beacons 1 and 2 are the midpoints of the white circles. If so you are dealing with 2 equilateral triangles with the side length r = distance between the two beacans.

The distance AB is twice the height of a triangle:
(Use Pythagorean theorem)

$h = \frac12 \cdot r \cdot \sqrt{3}$

Therefore

$|\overline{AB}|=2 \cdot \frac12 \cdot r \cdot \sqrt{3} = r \cdot \sqrt{3}$

Tot ziens!

3. Sorry, maybe my question wasn't clear enough. I am looking for the distance from a [random] candidate (3), with known distance to (1) and (2), to the beacons (A) and (B).

[ I was still able to calculate the distance AB myself ;-) ]

By the way, the triangle is not equilateral (or only by coincidence). The distance between the beacons (1) and (2) can vary.
(I'll update the picture to give a clearer view on the situation).