Shadow Tower happened in 1998.
Shadow Tower Abyss happened in 2003.
The Shadow of the Tower was created in 1972.
Shadow Tower was created on 1998-06-25.
Shadow Tower Abyss was created on 2003-10-23.
As the question is stated, Tom is standing IN THE TOWER'S SHADOW. If so, then Tom can't cast a shadow of his own, because he is not illuminated. Let's assume the question means to imply that Tom's shadow is measured AT THE SAME TIME that the shadow of the tower is measured, and kind of NEAR the tower, so that the sun casts both shadows from the same place in the sky. If this is a valid assumption, then the tower is 12 meters tall.
NO
After Shadow Pokemon Lab, it should open up. Exit wherever you are to go to the map. Just below SHadow POkemon Lab should be Realgam TOwer.
Shadow Blasters happened in 1990.
The Hound of Shadow happened in 1989.
Shadow of Memories happened in 2001.
Sky Shadow happened in 1990.
Shadow Squadron happened in 1995.