Idea: A 2m tall goalkeeper standing at the center of a gate throws himself against one of its upper corners. Find the approx. percentage of the diagonal length he is able to cover with stretched hands and estimate the number of ball diameters that would fit in the uncovered area. How much distance should the goalkeeper move to make for a 25% safer inclination angle to the ground to prevent injuries and what percentage of the original diagonal length would the new one be in this case?

```
from math import tan, atan2, degrees, radians
gate_width_m, gate_height_m = 7.32, 2.44
half_gate_width_m = gate_width_m / 2
soccer_ball_size5_d_cm = 22.5
# Sample human dimensions
human_height_cm, head_neck_height_cm, hand_length_cm, arm_length_cm = 168, 33.5, 69, 30
goalkeeper_height_m = 2
perc_higher_inclination_angle = 25
# Convert to meters
soccer_ball_size5_d_m = soccer_ball_size5_d_cm / 100
human_height_m, head_neck_height_m, hand_length_m, arm_length_m = [v / 100 for v in (human_height_cm, head_neck_height_cm, hand_length_cm, arm_length_cm)]
# Extrapolate to gauge goalkeeper body dimensions
scale_ratio = goalkeeper_height_m / human_height_m
goalkeeper_head_neck_m = scale_ratio * head_neck_height_m
goalkeeper_hand_length_m = scale_ratio * hand_length_m
goalkeeper_arm_length_m = scale_ratio * arm_length_m
goalkeeper_with_stretched_hands_m = goalkeeper_height_m - goalkeeper_head_neck_m + goalkeeper_arm_length_m / 2 + goalkeeper_hand_length_m
# Find gate center to corner diagonal (Pythagoras)
gate_center_to_corner_diag_m = (half_gate_width_m**2 + gate_height_m**2)**0.5
# Find coverage and ball diameters fitting
goalkeeper_diagonal_perc_coverage = (goalkeeper_with_stretched_hands_m / gate_center_to_corner_diag_m) * 100
ball_diameters_in_uncovered_diagonal = (gate_center_to_corner_diag_m - goalkeeper_with_stretched_hands_m) / soccer_ball_size5_d_m
# Find angle of inclination of the goalkeeper to the ground
goalkeeper_diag_to_ground_angle_deg = degrees(atan2(gate_height_m, half_gate_width_m))
#print(goalkeeper_diag_to_ground_angle_deg)
increased_angle = goalkeeper_diag_to_ground_angle_deg * (1 + perc_higher_inclination_angle/100)
distance_from_gate_post_for_better_angle_m = gate_height_m / tan(radians(increased_angle))
goalkeeper_distance_to_walk_to_satisfy_increased_angle_m = half_gate_width_m - distance_from_gate_post_for_better_angle_m
# New diagonal length and percentage of old
new_diag_length_m = (distance_from_gate_post_for_better_angle_m**2 + gate_height_m**2)**0.5
new_diag_length_as_perc_of_old = (new_diag_length_m / gate_center_to_corner_diag_m) * 100
print("""
Percent diagonal coverage by goalkeeper: %.2f%%
Ball diameters fitting in the uncovered diagonal: %.2f
Distance to move for a %d%% higher inclination angle to the ground: %.2fm
New diagonal length as percent of old diagonal length: %.2f%%
""" % (goalkeeper_diagonal_perc_coverage, ball_diameters_in_uncovered_diagonal, perc_higher_inclination_angle, goalkeeper_distance_to_walk_to_satisfy_increased_angle_m, new_diag_length_as_perc_of_old))
```

Percent diagonal coverage by goalkeeper: 59.13% Ball diameters fitting in the uncovered diagonal: 7.99 Distance to move for a 25% higher inclination angle to the ground: 0.96m New diagonal length as percent of old diagonal length: 82.72%

If the calculations are correct, moving ≈1m to the side reduces the diagonal to cover by ≈17.3%.