Many football game commentators harp about how much harder it is to kick field goals from the hash marks since the uprights have been made five feet narrower. The goal of this investigation is to see if there is any merit to the commentators argument that teams should take a penalty in order to have a "better angle" on the field goal kick.
According to the NCAA rules and regulations, the field measurements are as shown in the graph below. The controversy began when the uprights were changed from 23'4" to 18'6". Now the hash marks are in line with the uprights.
The figure below describes details needed for in order to find angle O.
The table below illustrated how angle O changes as the placement of the ball changes.
As indicated in the table, angle O is at its maximum when the ball is placed on the 6.3 yard line. From this information, I believe that in most cases, taking a penalty would not make the kick easier.