# D'Inverno Exercise: velocity between reference frames given angle of a rod

I'm trying an exercise from D'Inverno book "Introducing Einstein's Relativity" that says

S and S' are in standard configuration with $$v = \alpha c$$ $$(0 < \alpha < 1)$$. If a rod at rest in S' makes an angle of 45º with Ox in S and 30º with O'x in S', then find $$\alpha$$.

Well, I tried to do this thinking that there is an angle between the axis of the frames, i.e., 45º - 30º = 15º. But as they are in 'standard configuration', it means that the axis are parallel (and that the movement of S' is in the direction of positive x axis). So I don't see how the movement of S' with respect to S influences on the orientation of the rod from one frame to another. Any help in understanding this will be appreciated.

Note: The answer is $$\alpha = (2/3)^{\frac{1}{2}}$$

• Think about length contraction along the direction of relative motion. – G. Smith Jun 16 at 20:58
• Yes, I got it! Thank you! – Elismar Lösch Jun 16 at 21:27