Finding the co-ordinates of the points on a triangle

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SUMMARY

The discussion focuses on determining the coordinates of the third vertex of a triangle when two vertices are known, along with the lengths of all sides and one included angle. Participants suggest using either the equations of the lines forming the triangle's sides or applying the distance formula to establish simultaneous equations. The key methods involve solving for the unknown vertex using the known coordinates and lengths, leading to a system of equations that can be solved for the third vertex's coordinates.

PREREQUISITES
  • Understanding of coordinate geometry
  • Familiarity with the distance formula
  • Knowledge of simultaneous equations
  • Basic trigonometry, particularly regarding angles in triangles
NEXT STEPS
  • Study the distance formula in coordinate geometry
  • Learn how to solve simultaneous equations
  • Explore the properties of triangles, including the Law of Cosines
  • Investigate methods for deriving equations of lines from points
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Mathematicians, engineering students, and anyone involved in computational geometry or triangle-related calculations will benefit from this discussion.

tyroiusrtmaon
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So I've been trying to figure this out for quite a while and all the sources I've found on the internet haven't seemed to work. Basically what I have is the position of two points, I have all the sides and one of the included angles and I want to find the coordinates of the third vertex. I've tried several different approaches and none have really worked, I'd appreciate some help. Thanks in advance.
 
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Try setting all your data in a coordinate system...
 
tyroiusrtmaon said:
So I've been trying to figure this out for quite a while and all the sources I've found on the internet haven't seemed to work. Basically what I have is the position of two points, I have all the sides and one of the included angles and I want to find the coordinates of the third vertex. I've tried several different approaches and none have really worked, I'd appreciate some help. Thanks in advance.

"You have all the sides"? You could mean:

1. you have the equations for the lines that are the sides.
2. you have their length.

(1)If you have there equations, then you can find a common value of x and y that solves both of the equations. This is called simultaneous equations.

(2)If you have there length, then you could write L² = (X - x)² + (Y - y)² where little x and y are the co-ordinates of the 3rd vertex. And big X and Y are the co-ordinates of the known vertex. And L is the length between them that you have been given. You could do this for the lengths between each of the known vertices and the unknown one. Again, this would lead to simultaneous equations.

"and one of the included angles" Do you know where the angle is located? As in, do you know the two different sides that meet to create this angle?

Give us a bit more detail on your problem
 

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