In the sports of Basketball and Soccer your goal is to get a ball into a net. I've decided to calculate the number of degrees that you can make the shot within while still having the ball going into the net.
Soccer
*This assumes a 24 ft wide net and that you are in front of one of the net.
F(x) = 57.3(8/x)
Where x = distance from net in yards
("8/x" calculates radians, and multiplying by 57.3 converts that to degrees)
This outputs roughly:
05y: 91.7 deg
10y: 45.9 deg
15y: 30.6 deg
20y: 22.9 deg
25y: 18.3 deg
30y: 15.3 deg
40y: 11.5 deg
50y: 9.2 deg
As you can see, the further you get away from the net the substantially harder it is to make sure that you're shooting within the right range.
Basketball
*This assumes a 17" hoop, 9.4" ball and that you are aiming for the hoop, not the backboard. I am also considering the range in which the ball can hit the rim and still go in, which makes the arc that you can shoot into roughly 14.3" wide.
F(x) = 57.3(1.2/x)
Where x = distance from hoop in feet05 ft: 13.8 deg
10 ft: 6.9 deg
15 ft: 4.6 deg
20 ft: 3.4 deg
25 ft: 2.8 deg
30 ft: 2.3 deg
FREETHROW: 5.3 deg
THREE POINTS: 3.5 deg Ok, so if you play basketball and know what percentage of the time you make Freethrows you could theoretically calculate the amount of times you will land three pointers. Neat, huh? Just run this function:
F(x) = 3.5/(5.3/x)
Where x = percentage of time you make a freethrow (without the backboard) in decimal
Note: If you replace 3.5 with the degrees from another distance your result will correspond to that one.
Trigonometry sucks.
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