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How can I find the coordinates of the 4th point ($p_4$) only by the known coordinates of the other three points $(p_1,p_2,p_3)$ and the angles to them $(a,b,c)$ relative to the free line (l) through this 4th point? Distances to known points from the 4th point are unknown.

Please, see the pic

TShiong
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DmytroZ
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  • Welcome to MSE. You'll get a lot more help if you show that you have made a real effort to solve the problem yourself, even if you haven't made much progress. What are your thoughts? What have you tried? How far could you get? Where are you stuck? This question will likely be closed if you don't add more context. Please respond by editing the question body. Clarifications don't belong in the comments. – saulspatz Apr 24 '21 at 16:45

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I am answering just to clarify the question given the following figure you have $BC=a$, $BA=c$ and angles $\alpha=\widehat{BEC}$, $\beta=\widehat{BEA}$ (the line $l$ is useless you may say). Then to find the coordinate if $E$ you need to find the intersection of two cercles: they are the circumcircles of the triangles $CBE$ and $BEA$.enter image description here

Toni Mhax
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