Help!!!

[jeca86]

An observer stands at a point P, one unit away from a track. Two runners start at the point S in the figure and run along the track. One runner runs three times as fast as the other. Find the maximum value of the observer's angle of sight theta between the runners.

Am i suppose to maximize the tan theta? I dont know how to put up the figure.

 

[Gene]

If you can't put up a sketch of the figure by clicking twice on Code and typing between the boxes you will have to describe it. Is it an elipse? A circle? Are any distances given?
------------------
Gene

 

[jeca86]

         ____P
            l\?\
            l \  \
       1    l  \   \
            l   \    \ 
            l    \     \
            S_____\______\

 

[Gene]

Very good first try, but you have to un-check disable bbc codes at the bottom. would suggest yoy change your profile so they are not disabled. And there is no S shown. I assume it under P.
Runner B runs three times as fast.
Tan(A) = vt/1
Tan(B) = 3vt/1
Tan(B-A) = (tan(B)-tan(A))/(1+tan(A)*tan(B))
Can you take it from there?

 

[jeca86]

so then do i differentiate my answer from the difference formula for tangents?