# Calculating the angle of rotation

So i have the figure below:

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

but I'm not getting the same answer.

• I can see only ONE blue point in the figure. – 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 $$(4, 2)$$.
• @MattiP. Yes, applying that formula with the points exchanged leads to $-13.6441°$. – Aretino Sep 11 at 10:19
• Ah, now I recalculated: $$\tan^{-1}\left( \frac{2 \cdot 4.3589 - 4 \cdot 1}{4 \cdot 4.3589 + 2 \cdot 1} \right) \approx 13.6441^{\circ}$$ – Matti P. Sep 11 at 10:22