Mine Development & Surveying

EDM, Total Station & GPS

Resolving an EDM-measured slope distance into its horizontal and vertical components using the vertical angle.

PART 1

Topic Breakdown & Traps

The Engineering Principle

An EDM (electronic distance measurement) instrument — the heart of a total station — measures the straight-line slope distance to a prism. To map and level we need the horizontal distance and the vertical (height) difference, obtained by resolving the slope distance with the measured vertical angle: the horizontal component uses the cosine, the vertical component the sine. GPS gives 3-D coordinates directly but the same trigonometric resolution applies to any sloping measurement.

The Core Formula Matrix

Horizontal distance:

D = S cos α

.

Vertical (height) difference:

V = S sin α

S

= slope distance,

α

= vertical angle from the horizontal.

The ‘IIT Traps’

⚠
Horizontal uses cosine, vertical uses sine. Swapping them is the classic slope-reduction error.
⚠
** $α$ is measured from the horizontal**, not the vertical (zenith) — check the instrument convention.
⚠
Slope distance ≥ horizontal distance. If your 'horizontal' exceeds the slope distance, the trig is inverted.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

A total station measures a slope distance of

200 m

at a vertical angle of

3 0^{\circ}

. The horizontal distance is:

Q2MEDIUM2 Marks · NAT

A slope distance of

250 m

is measured at a vertical angle of

2 0^{\circ}

. The vertical height difference is ______ m. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

An EDM slope distance of

500 m

is observed at a vertical angle of

1 2^{\circ}

. The horizontal distance is ______ m. (Round off to two decimal places.)