Given. Three coal-seam outcrop points on a topographic contour map: A at 500 m, B at 400 m, C at 300 m elevation, with map positions as plotted on the source figure.
Find. The strike and dip of the (assumed planar) coal seam, and its outcrop trace across the mapped topography.
Check: the source page carries no printed scale bar or grid spacing (only bare contour labels), so an absolute dip ANGLE cannot be recovered without an assumption. The construction below is exact and scale-independent for the STRIKE; for the dip magnitude a representative 1:10,000 map scale (1 cm on the page = 100 m on the ground) is assumed and flagged — rescale the reported dip proportionally if the paper's true printed scale differs.
Fig. D — three-point construction: the 400 m structure contour (B–D) fixes the strike; the coal-seam outcrop trace (red) follows the topography, V-ing down-dip (toward the SE) across the valley on the right of the map.
Approach. Interpolate the point on line A–C that shares B's elevation; the line joining that point to B is a structure contour (fixes the strike). The dip direction is perpendicular to strike, toward lower elevation; the dip magnitude follows from the perpendicular spacing between two structure contours 100 m apart in elevation.
Locate the 400 m point on A–C. Since elevation varies linearly across a planar surface, and 400 m is exactly midway between A's 500 m and C's 300 m, the point D (elevation 400 m) is the midpoint of segment AC in map view.
Strike. Line B–D joins two points both at 400 m elevation, so it IS the 400 m structure contour on the seam — its trend is the seam's strike: \(\boxed{\text{strike} \approx \text{N}35^{\circ}\text{E}\ (034^{\circ}/214^{\circ})}\).
Dip direction. Perpendicular to strike, toward decreasing elevation (away from A, toward C's side of the map): \(\boxed{\approx 124^{\circ}\ (\text{SE})}\).
Dip magnitude. The perpendicular map distance between the 500 m contour (through A) and the 400 m contour (line B–D) corresponds to 100 m of elevation change. Measured on the source page this spacing is 3.74 cm; at the assumed 1:10,000 scale that is 373.8 m on the ground, so \(\delta = \arctan\!\left(\dfrac{100\ \text{m}}{373.8\ \text{m}}\right) = \boxed{15^{\circ}}\ \text{(assumed-scale value)}\).
(b) Outcrop pattern. Constructing further structure contours parallel to B–D at 100 m spacing and marking where each crosses the topographic contour of the SAME elevation traces the seam's outcrop across the whole map. Because the seam dips gently (≈15°, shallower than the mapped valley walls), the outcrop trace obeys the standard Rule of V's: it V's in the DOWN-DIP (SE) direction when it crosses the valley on the right side of the map, and swings the opposite way (up-dip, NW) around the closed hill contoured near point A, exactly as sketched in Fig. D.
Question D results
Quantity
Value
Strike
N35°E (034°/214°) — exact, scale-independent
Dip direction
≈124° (SE) — exact, scale-independent
Dip magnitude
≈15° SE (assumes 1:10,000 map scale — see check callout)
Outcrop pattern
V's down-dip (SE) crossing the valley; V's up-dip (NW) around the A-hill
