"Theory
and Results"
by Juan Chow, Maureen Kennedy,
Rebecca Tedford and Carrie Walker.
The
SOKKIA Set 6F theodolite projects a laser beam to a prism target and returns
a 3D coordinate set in the form of N, E, and Z.
Juan and Rebecca

The
theodolite requires a coordinate set as its starting position.
We choose due north as our Yo
coordinate, due east as our Xo coordinate, and Zo to be the vertical direction;
Xo, Yo, and Zo are all zeros at the theodolite measuring station.
a
Fig. 1. a = Azimuth
angle. Angle on the horizontal plane that diverges from Xo (in our case,
North). from the vertical above the theodolite to the line that defines
the slope distance S.

Ih is the height
of the theodolite. Th is the height of the prism target; because these
two heights are not equal and are not on the surface of the land, they
must be taken into account when calculating Z.
b
Fig. 2. b = Zenith angle. Angle
measured from above the theodolite down to the line that defines the slope
distance S. (See Fig. 3.) 
S Z
Fig. 3. S = Slope distance. The
direct distance from the theodolite to the prism target. Z = Height difference
between Zo and the height of the land at the prism target.
S = N / cosa sinb = E / sina
sinb
Z = Zo + Ih + S (cosb) ñ
Th (for our purposes, Zo = 0) 
a
asadsda
Fig. 4. Plan view of the relationship
among N, E, and a (azimuth angle).
N = Distance from the theodolite
to a point along the Yo axis that is perpendicular to the target.
= Yo + ( S sinb cosa)
E = Distance from the theodolite
to a point along the Xo axis that is perpendicular to the target
= Xo + ( S sinb sina)

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Maureen and Carrie 
. 