Angle-Distortion Equations in Special Relativity

Let's consider an object of triangular form $\Delta $\textit{ABC }moving in the direction of its bottom base \textit{BC} (on the $x-$axis), with speed $v$. The side \textit{\textbar BC\textbar }$= \quad \alpha $\textit{ is} contracted with the Lorentz contraction factor $C(v)=\sqrt {1-v^{2}/c^{2}} $ since \textit{BC} is moving along the motion direction, therefore \textit{\textbar B'C'\textbar }$= \quad \alpha C(v). $But the oblique sides \textit{AB }and \textit{CA} are contracted respectively with the oblique-contraction factors \textit{OC(v, B) }and\textit{ OC(v, }$\pi -C),$ where the \textbf{oblique-length contraction factor} is defined as: \[ OC(v,\theta )=\sqrt {C(v)^{2}\cos^{2}\theta +\sin^{2}\theta } . \] In the resulting triangle $\Delta A'B'C'$ one simply applies the Law of Cosine in order to find each distorted angle A', B', and C'. Therefore: \[ A'=\arccos \frac{-\alpha^{2}\cdot C(v)^{2}+\beta^{2}\cdot OC(v,A+B)^{2}+\gamma^{2}\cdot OC(v,B)^{2}}{2\beta \cdot \gamma \cdot OC(v,B)\cdot OC(v,A+B)}, \] \[ B'=\arccos \frac{\alpha^{2}\cdot C(v)^{2}-\beta^{2}\cdot OC(v,A+B)^{2}+\gamma^{2}\cdot OC(v,B)^{2}}{2\alpha \cdot \gamma \cdot C(v)\cdot OC(v,B)}, \] \[ C'=\arccos \frac{\alpha^{2}\cdot C(v)^{2}+\beta^{2}\cdot OC(v,A+B)^{2}-\gamma^{2}\cdot OC(v,B)^{2}}{2\alpha \cdot \beta \cdot C(v)\cdot OC(v,A+B)}. \] The angles A', B', and C' are, in general, different from the original angles$ A, B, $and $ C$ respectively. The distortion of an angle is, in general, different from the distortion of another angle.