Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in the figure. If R is chosen to minimize the length of the rope, Find the ratio

$\dfrac{\theta _1}{\theta _2}$

in terms of a and b where a is the length of PQ and b is the length of ST.