A solar station is to be built at ground level on the east-west line between two buildings. The distance between the two buildings is 100 meters, the height of the taller building is 80 meters, and the height of the smaller building is 40 meters. How far from the taller building should the station be placed in order to maximize the

number it will be in the sun on a day when the sun passes directly overhead? Note that :

(theta) = (pi) - (cot)^(-1) [(100-x)/(4)]

and find the value of x which maximizes theta.