Expert: Ahmed Salami - 6/18/2004

Question
Hi Ahmed

I'm trying to figure out a point's coordinates given that I know a number of values. I am assuming this point lies within a triangle of known points. I know the distance and angles between each of the vertices. From each point I have a reading (say % of signal strength).  For clarity lets cal each vertices ABC, (I'm making these values up but I hope you get my gist) if:

A---------B
|        /
| p   /
|    /
|  /
C

A-B = 6
A-C = 8
B-C = sqrt(AB^2 + AC^2) = 10

Co-ordinates:
A= 0,0
B = 6,0
C = 0,8

Angles given point A is 0,0 co-ordinates
B is on a bearing 90º from A
C is on a bearing 180 from A
(I'm assuming we can work out B to be but can be collected if needed)

So my question, how do I work out how far away from point A (0,0) is point P

given that point P is:
25% signal strength from A
15% strength from B
60^ strength from C

any help would be greatly appreciated;

Explored routes:
Equation of a circle so each intersects.
 {Find the intersects of the circles (signal % being the radius) between each points AB, AC, BC , thus giving three separate co-ordinates}
Triangulation, {never really got it}
Establishing the centre of a circle (centroid) {once  have the three co-ords from the intersect this seemed the only best way to get the mean co-ordinate}

Thoughts:
The problems I have with previous solutions, is that they require a 90 º angles
between points A and B. Although this is the case in my example it will not always be so.
In the same manner as a centroid of any triangle is established by  multiplying all x co-ords then devising by 3, likewise multiply the y and devise by 3 to get the y co-ords, is it then feasible that a much simpler solution should arise.  

Answer
Hi David,
I'm really sorry about the delay.
your question is a little bit involved but i would say i can't see anything impossible to get in the question.
Due to time, i would like you to just bring up a specific example with enough information which i would then solve and do a little more necessary explanation.
But i would say most of the times, just two distances are enough to define a point.
Sorry for any let down.
hope to hear from you.
Regards.