Exercise 1 solution

Variation: 2 degrees west of grid north, so grid to magnetic = add 2.

Legs (east, north in metres from a local origin):
  A: (450, 200) to (600, 350): dE = 150, dN = 150. Equal, so the line points exactly north-east.
     Grid bearing 045. Magnetic bearing 047.
  B: (300, 300) to (300, 100): dE = 0, dN = -200. Straight south.
     Grid bearing 180. Magnetic bearing 182.
  C: (700, 250) to (500, 450): dE = -200, dN = +200. North-west.
     Grid bearing 315. Magnetic bearing 317.
  D: (100, 500) to (400, 100): dE = 300, dN = -400.
     Angle from the south line = atan(300/400) = 36.9 degrees towards the east,
     so grid bearing = 180 - 36.9 = 143.1, about 143. Magnetic bearing about 145.

Distances (Pythagoras): A 212 m, B 200 m, C 283 m, D 500 m.

Method: the bearing is the clockwise angle from north. Work out which quadrant the leg lies in,
find the angle from the nearer north-south line using atan(across / along), then convert.