Sports announcers sometimes suggest that teams close to the goal line should take a penalty before allowing their field goal kickers to attempt a field goal when the ball is located close to or on the hash marks. According to their "reasoning", the penalty gives the field goal kicker a larger angle to the goal and thus increases the kicker's chances of making the field goal. We will examine this premise in the following discussion.
In the diagram below, segment AD represents the goal posts, which in college are 18.5 feet apart. The hash marks, indicated by the dashed line segments, are 40 feet apart. We will examine angle ABD where B is a point on the hash marks. According to the announcers' conjecture, as B moves closer to the goal posts, angle ABD should decrease. As B moves away from the goal posts, angle ABD should increase.
Click here for a GSP sketch that examines the announcers' claim.
The GSP sketch indicates that the opposite of the announcers' claim is true. As B moves closer to the goal posts, angle ABD actually increases until it reaches point E (in the end zone) where it begins to increase.
Click here for additional explanation.