I would write:

$\displaystyle \tan(\theta)=\frac{x}{50}$

Differentiating with respect time time $\displaystyle t$, we find:

$\displaystyle \sec^2(\theta)\frac{d\theta}{dt}=\frac{1}{50}\cdot \frac{dx}{dt}$

$\displaystyle \frac{dx}{dt}=50\sec^2(\theta)\frac{d\theta}{dt}$

Now plug in the given values:

$\displaystyle \frac{dx}{dt}=50\sec^2\left(\frac{\pi}{6} \right)\left(-\frac{9}{10} \right)$

So what do we get?