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[itex]\tan{\phi'}=\frac{1}{\gamma} \tan{\phi}[/itex]

where [itex]\phi[/itex] is the angle the rod makes with the x axis according to an observer in S.

so far I have [itex]\tan{\phi'} = \frac{y'}{x'}=\frac{y}{\gamma(x-vt)}=\frac{1}{\gamma} \frac{y}{x-vt}[/itex]

if i could just get rid of that vt, i'd be there but i can't seem to get it to go away...