Coordinates of the three points and the three angles relative to the x-axis
Variables are known only $(x_1,y_1)$; $(x_2,y_2)$; $(x_3,y_3)$; angle $A$; angle $B$; angle $C$
How to find the $(x_4,y_4)$ coordinates?
2026-04-11 21:23:25.1775942605
Coordinates of the three points and the three angles relative to the x-axis
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You have three linear equations to determine two unknowns ($i=1,2,3$, $A_{1,2,3}=A,B,C)$: $$ \frac{y_4-y_i}{x_4-x_i}=\pm\tan A_i,\tag1 $$ Solve two of them to find four pairs of solution and check which one satisfies the third equation.
PS. In $(1)$ I assumed that the given angles are unsigned and not equal to $\frac\pi2$. If the angles are signed all three pairs of equations have to result in the same solution, so that either the problem is unsolvable or any pair of equations suffice.