The back of the free throw line is 13 feet 9 inches from the center of the goal.
FYI: The standard goal is 18 inches (ID).
The goal is attached to a 6 inch bridge .
The bridge is attached to the backboard.
The center of the goal is 1 foot 3 inches from the front of the backboard.
This makes the backboard 15 feet from the back of the free throw line.
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The question is not exactly clear however, the free throw line is 15 feet from the rim. The rim is 10 feet above the ground.