I need to calculate the angle between two sides, I have the length of A & B sides, but don't know how to find the angle...

Both sides are the same length.

I can get the start and end vectors of each side, I can also get the center values of each side.

Here's an image better describing my question:

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  • $\begingroup$ We need more information. $\endgroup$ – Ali Caglayan Sep 1 '13 at 1:31
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    $\begingroup$ You only know two sides and no angle. This is not enough information to calculate that angle. $\endgroup$ – imranfat Sep 1 '13 at 1:31
  • $\begingroup$ What additional information do you need? $\endgroup$ – Shannon Hochkins Sep 1 '13 at 1:34
  • $\begingroup$ As I said I don't know! :( but what else do you need to calculate the angle? I'll see if I can get it @Alizter $\endgroup$ – Shannon Hochkins Sep 1 '13 at 1:34
  • $\begingroup$ What else do you need @imranfat? $\endgroup$ – Shannon Hochkins Sep 1 '13 at 1:39

Assuming you have points: $$A=(A_x, A_y),\ B=(B_x,B_y)$$ And two equal sides with length $l$ originating from a shared point $O=(0,0)$, then the angle between $AO$ and $BO$ will be: $$\cos\theta = \frac{AO\cdot BO}{l^2}$$ $$\theta = \cos^{-1} \left(\frac{A_xB_x+A_yB_y}{l^2}\right)$$ This is just a particular case of the dot product.

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  • $\begingroup$ Wow, that's great! $\endgroup$ – Shannon Hochkins Sep 1 '13 at 1:59
  • $\begingroup$ so what would A/b be actually equal to? the end point of each side? $\endgroup$ – Shannon Hochkins Sep 1 '13 at 2:01
  • $\begingroup$ @ShannonHochkins - yes. A could be, say (1,2) And B would be say (2,1), both would have the same distance from the origin (0,0). $\endgroup$ – nbubis Sep 1 '13 at 2:04
  • $\begingroup$ Just to be clear here, those coordinates of the endpoints were NOT given in the question. And if these coordinates were, say A(4,1) and B(1,4), that angle would be different! $\endgroup$ – imranfat Sep 1 '13 at 3:18
  • $\begingroup$ @imranfat - I'm sure no one would have thought otherwise. That's the meaning of the word "say": this is just a particular example. $\endgroup$ – nbubis Sep 1 '13 at 4:35

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