The rate of change of the angle, $\displaystyle \frac{d\theta}{dt}$, needs to be expressed in radians/minute:
$\displaystyle \frac{d\theta}{dt}=\frac{0.27\pi}{180}=0.00471$
So $\displaystyle \frac{dx}{dt}=-80\csc^2{\theta}\frac{d\theta}{dt}=-80\left(\frac{100}{80}\right)^2(0.00471)=0.589$ feet per minute
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