Please help Assume that the distance between the goal posts

Please help.

Assume that the distance between the goal posts, 19.5 feet, is the length of an arc on a circle of radius 50 yards as show in the figure. The kicker aims to kick the ball midway between the uprights. To score a field goal, what is the maximum number of degrees that the actual trajectory can deviate from the intended trajectory? What is the maximum number of degrees for a 20-yard field goal?

Solution

raw sector of a circle with arc length 19.5 ( 19.5/3 foot = 6.5 yard) and radius 50 yards

In degrees, the length of the arc length of a circle is: 2pi*r*theta/360

6.5 = 2pi*50*theta/360

theta = 6.5*360/2pi*50 = 7.44 deg

Goal keeper aims at middle, so we need to half our level of error = 7.44/2 = 3.72 deg

Actual trajectory can deviate by 3.72 deg

Now if the radius = 20 yards

In degrees, the length of the arc length of a circle is: 2pi*r*theta/360:

theta = 6.5*360/2pi*20

= 18.62 deg

Goal keeper aims at middle, so we need to half our level of error = 18.62/2 = 9.31 deg

Actual trajectory can deviate by 9.31 deg