SUR 3520: Measurement Science
Spring 2007 – Section 4218
Assignment No. 4
Due Date: February 12, 2007
Student UFID: 62441221
Student Name: Shane Christy
4.1 Find the inverse of
=
10
4
5
3
A


3
.
4
.
5
.
1
4.2 Use firstorder terms of Taylor’s expansion series to iteratively determine the
equation of a circle that passes through the points (9.4, 5.6), (7.6, 7.2), and (3.8, 4.8).
Take initial approximation for unknowns of the circle equation: center point (x
c
,y
c
) =
(7, 4.5) and radius (r) = 3; circle equation is
2
2
2
94
.
2
)
39
.
4
(
)
72
.
6
(
=

+

y
x
4.3 In Problem 1.6 compute the estimated error in the overall distance as measured by
both the 100ft tape.
.
0045
.
)
004
(.
)
0021
(.
2
2
ft
±
=
+
4.4 A slope distance is observed as 1506.843 ± 0.009 m. The zenith angle is observed as
92°37
’
29
”
± 8.8
”
. What are the horizontal distance and its uncertainty?
m
ce
is
HorzontalD
S
S
m
S
H
H
H
0095
.
262
.
1505
tan
0095
.
)
00294
(.
)
00899055
(.
)
"
8
.
206264
"
8
.
8
)
29
37
2
sin(
843
.
1506
(
)
009
.
99895
(.
2
2
2
±
=
±
=
+
=
•



+
•
=
4.5 A rectangular parcel has dimensions of 538.056 ± 0.005 m by 368.459 ± 0.004 m.
What are the area of the parcel and the uncertainty in this area?
University of Florida
Geomatics – SFRC
2
2
2
)
c
(
)
(
r
y
y
xc
x
=

+

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SUR 3520: Measurement Science
Spring 2007 – Section 4218
2
2
2
2
3
198252
068
.
3
)
004
.
459
.
368
(
)
005
.
056
.
538
(
m
m
Area
S
S
A
A
±
=
±
=
+
=
4.6 A racetrack is measured in three simple components; a rectangle and two semicircles.
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 Spring '09
 Kiker
 Distance, Measurement Science

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