How to find the coordinates of the third vertex?

Question

Programming

Given:

• coordinates of the other two vertices A _x A _y and B _x B _y
• angles α and β
• lengths of all sides AB , BC , AC

Find the coordinates of the third vertex C _x C _y .

Please help me find the formula.

Answer 1

Tyts

Answer 2

Tyts №2

Answer 3

www.kakprosto.ru/kak-115840-kak-nayti-vershiny-uglov

Answer 4

Equation of a straight line
Solving triangles

I'm sure I messed up something, but I think the principle is clear.

Answer 5

I'll add my answer.
Edited as a google sheet.
Triangle find third coordinates
Just substitute your coordinates of 2 points and the lengths of the sides, we get the result.

Answer 6

My implementation in Pascal of solving the problem of finding the third vertex of a right triangle for the case when given:
Got the idea for the solution here .
In this formulation, the problem has two solutions.

Two solutions on the example of the Egyptian triangle

block diagram

Program output