A hole is never where the collar says it is. Give it its survey and this walks it down by minimum curvature — the arc between two stations rather than a straight line, which is what every mine and well planning package uses.
Dip is measured from horizontal and is negative downward, as a mining survey is written: −90 is straight down, 0 is horizontal. Azimuth is degrees from north, clockwise.
Where is the hole at 137 m? Interpolating between survey stations along the same arc — not along the straight line between them — is the whole point of a desurvey.
A hole almost never crosses a structure square, so the intercept is longer than the thing itself. True thickness is the intercept times the cosine of the angle between the hole and the pole to the plane — an intercept quoted as a width is the commonest overstatement in exploration.
Between two stations the hole is assumed to follow a circular arc in the plane containing both directions. The angle between those directions is the dogleg β:
cos β = cos(I₂−I₁) − sin I₁ · sin I₂ · (1 − cos(A₂−A₁))
RF = (2/β) · tan(β/2) → 1 as β → 0
ΔN = (ΔMD/2)(sin I₁ cos A₁ + sin I₂ cos A₂) · RF
ΔE = (ΔMD/2)(sin I₁ sin A₁ + sin I₂ sin A₂) · RF
ΔTVD = (ΔMD/2)(cos I₁ + cos I₂) · RF
I is the inclination from vertical, so a dip of −60 from horizontal is an inclination of 30. The ratio factor RF is what makes it an arc: with no change in direction it is exactly 1 and the method collapses to the straight balanced-tangential answer, which is the check to run first on any implementation.
Dogleg severity is β over a standard length — 30 m here, as metric mining quotes it. Above about 3° per 30 m a hole is deviating enough to matter for a wedge, a survey tool, or the geometry of an intercept.
Survey stations are not the truth either: they are measurements with their own error, typically ±0.2–0.5° in dip and worse in azimuth near vertical, where azimuth becomes ill-defined. A hole surveyed only at the collar has not been surveyed.
Structures logged in the core as alpha and beta need this hole's attitude to become real orientations — that conversion is in Core logging, and the desurveyed attitude at the logged depth is what it needs.