Fun math problem!!

This looks like a tricky problem at first, but if you look at it for a min, then you can get it.

A cop car is 60m in front of the wall.  If the siren light is spinning at 20 revolutions per min, and a light beam from the siren light hits the wall at a 60deg angle (meaning the angle between the wall and the light beam is 60deg), find the speed the light beam is moving along the wall at that inst moment.

SHOW ALL WORK!!!

It CAN be done with the information provided, so don't complain.

___x___
\pi/3 |
 \    |
  \   |l=60m
   \  |
    \ |
     \|<--a=pi/6
     car
da/dt=2*pi/3s^-1

x=tan(a)*l
dx/dt=l*sec(a)^2*da/dt
dx/dt=(60m)*sec(pi/6)^2*(2*pi/3s^-1)
dx/dt=(pi*40m/s)*(sqrt(3)/2)^2
dx/dt=(pi*40m/s)*3/4
dx/dt=pi*30m/s