Geometry

We could use some fancy math here, but let's not.

Since a boy 6 feet tall casts a shadow 4 times his height (24 ft.), the flagpole must do the same.

Then the flagpole's shadow must be 4 times its height.

Then dividing 200 by 4, the height of the flagpole must be 50 ft.

And that it. No fuss, no muss.