please help.. pretty please?
note that on a right triangle, we have $\displaystyle \tan\theta=\frac{b}{a}$ where $\displaystyle b$ is the opposite side and $\displaystyle a$ is the adjacent side.
thus, from your figure, we have $\displaystyle \tan\theta=\frac{d}{3} \Rightarrow d = 3\tan\theta$..
now, how come that $\displaystyle \theta = \pi t$?
it was said that light spans a complete rotation (1 rev = $\displaystyle 2\pi$) every two minutes and thus the rate of revolution is $\displaystyle \pi$ per minute.
so, at time t minutes, the light spans $\displaystyle \pi$ times that time $\displaystyle t$, and that is the angle of rotation, thus we have $\displaystyle d = 3\tan(\pi t)$
aww, you were using $\displaystyle x$.. well it is just the same.. they are just dummy variables.