I can't seem to figure out how to set up this problem. I'm a bit confused on the relationship between the variables here; I've seen a similar problem involving a searchlight but the angle of $\theta$ at which the beam leaves the light was given. Without that I'm not sure how to manipulate the information given.
The problem reads: A searchlight is 100m from the nearest point on a straight highway. As it rotates the searchlight casts a horizontal beam that intersects the highway in a point. If the light revolves at a rate of pi/6 rad/s, find the rate at which the beam sweeps along the highway as a function of $\theta$. For what value of $\theta$ is this rate minimized?
I don't need the problem solved for me, I can do that, I just don't know how to set this up. The relationship is confusing to me. Thanks.