# Finding the co-ordinates of the points on a triangle

by tyroiusrtmaon
Tags: coordinates, points, triangle
 P: 1 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.
 P: 7 Try setting all your data in a coordinate system...
P: 163
 Quote by tyroiusrtmaon 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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