Tangential Relations between Distorted Acute Angles vs. Original Acute Angles of a Traveling Right Triangle in Special Relativity

Let's consider a traveling right triangle $\Delta $\textit{ABC} ($\angle A=\pi /2)$, with the speed $v$, and one of its legs \textit{AB} along the motion direction on the $x-$axis. After contraction of the side $AB$ with the factor C(v), and consequently contraction of the oblique side $BC$ with the oblique-contraction factor \[ OC(v,\theta )=\sqrt {C(v)^{2}\cos^{2}\theta +\sin^{2}\theta } , \] one gets the right triangle $\Delta A'B'C'$ with the following tangential relations between distorted acute angles vs. original acute angles of the right triangle: \[ \tan B'=\frac{\tan B}{C\left( v \right)}, \] \[ \tan C'=\tan C\cdot C\left( v \right), \] where $C(v)=\sqrt {1-\frac{v^{2}}{c^{2}}}_{\, \, }$is the Lorentz contraction factor, and $c$ is the speed of light in vacuum.