- #1

Herbascious J

- 165

- 7

- TL;DR Summary
- What would be a simple (as possible) equation to determine the distance between two apexes of two three-sided pyramids which have identical bases, but unique apexes. You are only given the distances between points, no angles.

A way to imagine this problem to stand on a plane. You have chosen three points on that plane to create a triangle-base and from these three points you can make distance measurements in any direction. You know the distance between each of the three points of the base, but you do not yet know any angles, and you will not be allowed to calculate these. Above you are two points suspended high in the air. You may imagine that each of these points could be their own apex of a three sided pyramid with the triangle base you have on the ground plane. You would like to know the distance between these two apexes precisely, but you can not measure it directly. You may however, measure the distance to each of the apex points above you from each of the the three points you have on the ground plane. You will never measure angles, only distances between these 5 points, and the only distance you may not measure directly is between the two points hovering high in the air. How do you find this distance?