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Q: 3 D Trigonometry ( Answered 5 out of 5 stars,   3 Comments )
Subject: 3 D Trigonometry
Category: Science > Math
Asked by: mahamannu-ga
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: livioflores-ga on 12 Jul 2006 20:54 PDT
Rated:5 out of 5 stars

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:

I hope this helps you. Feel free to request for a clarification if you
need it before rate this answer.

Best regards,
mahamannu-ga rated this answer:5 out of 5 stars

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: eiffel-ga on 13 Jul 2006 03:09 PDT
Mahamannu-ga, your researcher livioflores-ga 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: ansel001-ga on 13 Jul 2006 22:26 PDT

Great answer!  What did you use to create the graph?
Subject: Re: 3 D Trigonometry
From: livioflores-ga on 29 Jul 2006 20:31 PDT
I used Microsoft Paint.

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