Finding the xyz Coordinates of Point C in an Isosceles Triangle

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In summary, the conversation discusses finding the coordinates of point C in an isosceles triangle with known coordinates of points A and B. The triangle is on a plane, so only xy coordinates are needed. The measure of angle ABC is given as m, and it is mentioned that angle B must lie on the perpendicular bisector of AC. An equation for finding the coordinates of C is not provided, but it is mentioned that if angle B has measure m, then the other two angles have measure 90-m/2.
  • #1
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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  • #2
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?
 
  • #3
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.
 
  • #4
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)
 

What is the purpose of finding xyz coordinates?

The purpose of finding xyz coordinates is to determine the location of a point or object in three-dimensional space. This information can be used in various fields such as engineering, physics, and geography to accurately describe the position of an object or to calculate distances and angles.

What tools or techniques are used to find xyz coordinates?

The most common tools and techniques used to find xyz coordinates include using a coordinate system, such as Cartesian coordinates, and measuring devices like rulers, protractors, and GPS systems. Advanced methods like laser scanning and photogrammetry can also be used for more precise measurements.

Can xyz coordinates be used in both 2D and 3D space?

Yes, xyz coordinates can be used in both 2D and 3D space. In 2D space, only two coordinates (x and y) are needed to describe the location of a point, while in 3D space, three coordinates (x, y, and z) are required. However, the principles and techniques used to find xyz coordinates are the same in both 2D and 3D space.

What are some practical applications of finding xyz coordinates?

Finding xyz coordinates has many practical applications, such as in navigation and mapping, creating 3D models of objects and environments, and in determining the position of objects in robotics and computer graphics. It is also used in surveying, construction, and geological mapping.

Are there any limitations or challenges when finding xyz coordinates?

One limitation of finding xyz coordinates is that it assumes a flat, horizontal surface, which may not always be the case in real-world scenarios. Additionally, external factors such as weather conditions and measurement errors can affect the accuracy of the coordinates. It is important to consider these limitations and challenges when using xyz coordinates for any application.

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