# Special Relativity - Finding the angle θ measured in the frame S

[Question] Frame $$S'$$ moves with velocity $$V$$ in the $$x$$-direction relative to frame $$S$$. A rod in the frame $$S'$$ lying on the $$x'-y'$$ plane makes an angle $$\theta'$$ with respect to the forward direction of motion.

What is the angle $$\theta$$ as measured in $$S$$?

$$\begin{cases} ct' = cosh(\phi)ct - sinh(\phi) x \\ x' = -sinh(\phi)ct + cosh(\phi)x \\ y' = y \\ z' = z\end{cases}$$
• @verdelite , after viewing the different question from the recommended book, I arrived at the exact same answer where $\theta = arctan(\gamma tan(\theta '))$ once I went through the exact same answering process as the solution key. What do you think of the answer? Can the book's solution apply completely to this question? Perhaps, my biggest question is can I simply - and conveniently - throw out the $x'-y'$ part of information out of my solution? Thank you for your help and recommendation! – Athenian Nov 23 '19 at 3:34