title: Triangulating coordinates with an equation
body: <p>Ok, I know this sounds really daft to be asking here, but it is programming related.</p>
  
  <p>I'm working on a game, and I'm thinking of implementing a system that allows users to triangulate their 3D coordinates to locate something (eg for a task).
  I also want to be able to let the user make the coordinates of the points they are using for triangulation have user-determined coordinates (so the location's coordinate is relative, probably by setting up a beacon or something).</p>
  
  <p>I have a method in place for calculating the distance between the points, so essentially I can calculate the lengths of the sides of the triangle/pyramid as well as all but the coordinate I am after.
  It has been a long time since I have done any trigonometry and I am rusty with the sin, cos and tan functions, I have a feeling they are required but have no clue how to implement them.</p>
  
  <p>Can anyone give me a demonstration as to how I would go about doing this in a mathematical/programatical way?</p>
  
  <p>extra info:
  My function returns the exact distance between the two points, so say you set two points to 0,0,0 and 4,4,0 respectively, and those points are set to scale(the game world is divided into a very large 3d grid, with each 'block' area being represented by a 3d coordinate) then it would give back a value at around 5.6.</p>
  
  <p>The key point about it varying is that the user can set the points, so say they set a point to read 0,0,0, the actual location could be something like 52, 85, 93. However, providing they then count the blocks and set their other points correctly (eg, set a point 4,4,0 at the real point 56, 89, 93) then the final result will return the relative position (eg the object they are trying to locate is at real point 152, 185, 93, it will return the relative value 100,100,0). I need to be able to calculate it knowing every point but the one it's trying to locate, as well as the distances between all points.</p>
  
  <p>Also, please don't ask why I can't just calculate it by using the real coordinates, I'm hoping to show the equation up on screen as it calculates the result.7</p>
  
  <p>Example:
  Here is a diagram
  <img src="https://i.stack.imgur.com/9vss7.png" alt="Example Diagram"></p>
  
  <p>Imagine these are points in my game on a flat plain.
  I want to know the point f.
  I know the values of points d and e, and the sides A,B and C.</p>
  
  <p>Using only the data I know, I need to find out how to do this.</p>
  
  <p>Answered Edit:</p>
  
  <p>After many days of working on this, Sean Kenny has provided me with his time, patience and intellect, and thus I have now got a working implementation of a triangulation method.</p>
  
  <p>I hope to place the different language equivalents of the code as I test them so that future coders may use this code and not have the same problem I have had.</p>