

Subject:
3 D Trigonometry
Category: Science > Math Asked by: mahamannuga List Price: $10.00 
Posted:
12 Jul 2006 14:08 PDT
Expires: 11 Aug 2006 14:08 PDT Question ID: 745715 
Given the shortest distance to a plane P from a point P1, not in plane P, and given distances from point P1 to 2 points P2 and P3 on that plane P, is it possible to get the distance from P2 to P3, with no angle information what so ever. I'd prefer a link and the formula if one exists. What am I reaching at is 2 sides of a triangle, the 3rd being what I need to find, without the angle information between the 2 known sides. 

Subject:
Re: 3 D Trigonometry
Answered By: liviofloresga on 12 Jul 2006 20:54 PDT Rated: 
Hi!! You cannot determine the distance from P2 to P3 because you are not giving enough info for that: You have a point P1 and its distance to the plane P; this gives you the length of the perpendicular segment from the plane to P1. Regarding the point P2 you know its distance D2 from P1; this means that P2 is on a sphere centered on P1 with a radius D2; but you also know that it is on the plane P, then P2 is in the intersection between the sphere and the plane, that is P2 is on a circle on plane P. No more info regarding P2 is given. The same happens with P3. This gives you infinite possibilities for the points P2 and P3 that satisfy the problem criteria. For example if the distances from P2 to P1 and P3 to P1 (D2 and D3) are the same this does not mean that P2 and P3 are the same point, but they are on the same circle centered on the point where the normal to the plane P that contains P1 intersects the plane P. This means that, with the given data, P2 and P3 are not completely defined, this is why you cannot solve the problem, because you need more info to set P2 and P3 on the plane P; then knowing where P2 and P3 are you will be able to find the distance between them. I made the following graph with the hope that it can illustrate the problem for you: http://www.geocities.com/artistaflores/mahamannu.JPG I hope this helps you. Feel free to request for a clarification if you need it before rate this answer. Best regards, liviofloresga 
mahamannuga
rated this answer:
Thanks. This is my first time posting a question on google Answer and I am mighty impressed. Did you put in all the effort for 10 bucks ?? 

Subject:
Re: 3 D Trigonometry
From: eiffelga on 13 Jul 2006 03:09 PDT 
Mahamannuga, your researcher liviofloresga actually put in all that effort for $7.50, which is the researcher's share of the price paid. 
Subject:
Re: 3 D Trigonometry
From: ansel001ga on 13 Jul 2006 22:26 PDT 
Livioflores, Great answer! What did you use to create the graph? 
Subject:
Re: 3 D Trigonometry
From: liviofloresga on 29 Jul 2006 20:31 PDT 
I used Microsoft Paint. 
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