We proceed to optimize this function of two variables a and theta, using the calculus approach of setting the respective partial derivatives with respect to a and theta equal to 0 and solving for values of a and theta which make these partial derivatives equal to 0. We use our contour plot to obtain an initial starting point for our root finding algorithm.

Input := 


Remove[theta]

Input := 


axrange[a_,theta_] = D[xrange[a,theta],a];

thetaxrange[a_,theta_] = D[xrange[a,theta],theta];

Input := 


sol = FindRoot[{axrange[a,theta]==0,

			thetaxrange[a,theta]==0},

		{a,2000},{theta,.6}]

Output =


{a -> 1623.8, theta -> 0.523599}

Input := 


position = {-a, Sqrt[3] a}/.sol//N

Output =


{-1623.8, 2812.5}

Input := 


distance = Sqrt[position[[1]]^2 + position[[2]]^2]/5280

Output =


0.615075

Input := 


xrange[a,theta]/.sol//N

Output =


3247.6