Finding the xyz Coordinates of Point C in an Isosceles Triangle

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Discussion Overview

The discussion revolves around determining the xyz coordinates of point C in an isosceles triangle ABC, where AB = BC and angle ABC is specified. The context includes a computer programming application, with initial confusion regarding the dimensionality of the problem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant seeks equations to find the coordinates of point C based on the given triangle properties.
  • Another participant notes that in 3D space, a unique point cannot be determined due to the existence of infinitely many triangles in different planes.
  • A clarification is made that the triangle is actually on a plane, thus only xy coordinates are needed.
  • It is mentioned that if angle B measures m, then the other two angles measure 90 - m/2, and that point B must lie on the perpendicular bisector of AC.

Areas of Agreement / Disagreement

Participants express differing views on the dimensionality of the problem, with some initially assuming a 3D context while others clarify that the triangle is planar. The discussion remains unresolved regarding the specific equations needed to determine the coordinates of point C.

Contextual Notes

There is a lack of clarity regarding the implications of the angle measure and how it relates to the triangle's configuration. The initial assumption of needing xyz coordinates may have led to confusion about the problem's requirements.

Sikz
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Finding xyz coords of...

Given: ABC is an isosceles triangle; AB=BC; A(x,y,z); B(x',y',z'); m<ABC=m

I need, based on this information, a way to get the xyz coordinates of C. It's for a computer program I'm writing, and I'm afraid I'm rather unknowlegable about how to solve this type of problem- could someone please give me (an) equation(s) for this? The way those equation(s) work would be appreciated as well, but the equation(s) by themselves are all I really NEED.

Thank you very much.
 
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Unfortunately, given that you have expressed this in 3d space you will not be able to find a unique point which completes your triangle. There will be infinitely many triangles, each laying in a different plane.

I am not sure what your constriction
m<ABC=m

means, could you elaborate on that?
 
Ah yes, such a silly mistake. I assumed I would need xyz coords since the program deals with 3d space, but the triangle is on a plane... I actually only require xy coords.

And by m<ABC=m I meant "measure of angle ABC = m". Since I am unaware of the way to type a proper angle symbol, I used < :P.
 
Well, if angle B has measure m, then the other two angles have measure 90-m/2. Does that help?

(Also, B must lie on the perpendicular bisector of AC)
 

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