So i have the figure below:

enter image description here

and i want to find the angle $a$ as shown in green. I have the coordinates of the blue points where

$x_i,y_i = (4,2)$ and $x_j,y_j = (4.3589, 1)$

According to the answer, $a$ is 13.6441 degrees, but i do not know how to work it out.

I used the formula

enter image description here

but I'm not getting the same answer.

  • $\begingroup$ I can see only ONE blue point in the figure. $\endgroup$ – Aretino Sep 11 at 10:03

Your formula is fine, but you must switch your points, because $(x_1,y_1)$ in that formula refers to the point before rotation, which in your case is $(4.3589, 1)$, while $(x_2,y_2)$ refers to the point after rotation, which in your case is $(4, 2)$.

  • $\begingroup$ This should only flip the sign of the angle, no? $\endgroup$ – Matti P. Sep 11 at 10:17
  • $\begingroup$ @MattiP. Yes, applying that formula with the points exchanged leads to $-13.6441°$. $\endgroup$ – Aretino Sep 11 at 10:19
  • $\begingroup$ Ah, now I recalculated: $$ \tan^{-1}\left( \frac{2 \cdot 4.3589 - 4 \cdot 1}{4 \cdot 4.3589 + 2 \cdot 1} \right) \approx 13.6441^{\circ} $$ $\endgroup$ – Matti P. Sep 11 at 10:22
  • $\begingroup$ @Aretino strange, shouldn’t it be (4,2) for the point before rotation (black axis) and (4.3589,1) after rotation? Is the formula valid? Cause I found it in some other post. $\endgroup$ – Maxxx Sep 11 at 10:24
  • $\begingroup$ @Maxxx Your rotation is counterclockwise: just draw both points in the diagram and check which one is the start and which is the end. $\endgroup$ – Aretino Sep 11 at 10:32

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