A statue is 100 feet tall and stands on a 30 ft. pedestal. How far from the base should a man stand so that he can photograph the statue with largest possible angle ? Assume that the camera level is 5 ft.
If the man stands x ft away, then let
θ be the angle which subtends the statue and pedestal
α be the angle which subtends only the pedestal.
You want to maximize θ-α. So, let
f(x) = θ-α = arctan(125/x)-arctan(25/x)
df/dx = 100(3125-x^2)/((x^2+625)(x^2+15625))
Looks pretty nasty, but you can see that dy/dx=0 when x^2 = 3125
so, the man must stand about 56 ft away
Any farther, and the statue needs less of an aperture
Any closer, and the pedestal takes up too much of the angle.