Exercise 3 solution (Python)

import math

def grid_bearing(e1, n1, e2, n2):
    """Clockwise angle from grid north, 0 to 360."""
    return math.degrees(math.atan2(e2 - e1, n2 - n1)) % 360

def distance(e1, n1, e2, n2):
    return math.hypot(e2 - e1, n2 - n1)

def grid_to_magnetic(grid, variation_w):
    return (grid + variation_w) % 360

def magnetic_to_grid(mag, variation_w):
    return (mag - variation_w) % 360

def drift(error_degrees, metres):
    return metres * math.tan(math.radians(error_degrees))

legs = [(450, 200, 600, 350), (300, 300, 300, 100), (100, 500, 400, 100),
        (700, 250, 500, 450), (0, 0, 10, -10)]
for leg in legs:
    g = grid_bearing(*leg)
    print(round(g), round(distance(*leg), 1), round(grid_to_magnetic(g, 2)))

g = magnetic_to_grid(128, 2)
print(g, (g + 180) % 360)
print(round(drift(3, 800), 1), round(drift(5, 500), 1))

Output:
45 212.1 47
180 200.0 182
143 500.0 145
315 282.8 317
135 14.1 137
126 306
41.9 43.7

atan2(across, along) takes care of the quadrant for you; the % 360 turns a negative angle into the
matching positive bearing (for example -90 becomes 270).