978-0134604657 Chapter 11

11 COORDINATE GEOMETRY IN SURVEYING CALCULATIONS

Asterisks indicate problems that have partial answers given in Appendix G.

11.1 The X and Y coordinates (in meters) of station Shore are 246.873 and 659.457,

respectively, and those for station Rock are 437.854 and 973.482, respectively. What

are the azimuth, bearing, and length of the line connecting station Shore to station Rock?

11.2 Same as Problem 11.1, except that the X and Y coordinates (in feet) of Shore are 5048.64

and 3278.59, respectively, and those for Rock are 3303.33 and 5876.93, respectively.

*11.3 What are the slope, and y-intercept for the line in Problem 11.1?

11.4 What are the slope, and the y-intercept for the line in Problem 11.2?

*11.5 If the slope (XY plane) of a line is 0.800946, what is the azimuth of the line to the nearest

second of arc? (XY plane)

11.6 If the slope (XY plane) of a line is −0.3250683, what is the azimuth of the line to the

nearest second of arc? (XY plane)

*11.7 What is the perpendicular distance of a point from the line in Problem 11.1, if the X and

Y coordinates (in meters) of the point are 422.058 and 947.653, respectively?

31 17 38.6 ; 337.2636m

By (11.12): 120.502sin0 00 45.7 0.0748

 

  

 

  

SR

Az SR

SP

(*)

11.8 What is the perpendicular distance of a point from the line in Problem 11.2, if the X and

By (11.12): 1153.278sin0 00 59.3 0.117

 

  

SP

*11.9 A line with an azimuth of

105 46 33

 



from a station with X and Y coordinates of 5885.31

and 5164.15, respectively, is intersected with a line that has an azimuth of

200 31 24

 



from a station with X and Y coordinates of 7337.08 and 5949.99, respectively. (All

coordinates are in feet.) What are the coordinates of the intersection point?

11.10 A line with an azimuth of 37°30′48″ from a station with X and Y coordinates of 1234.87

and 898.56, respectively, is intersected with a line that has an azimuth of 314°51′43″

from a station with X and Y coordinates of 2034.79 and 962.48, respectively. (All

coordinates are in feet.) What are the coordinates of the intersection point?

11.11 Same as Problem 11.9 except that the azimuth of the first line is 43°31′06″ and the

azimuth of the second line is 331°06′00″.

11.12 In the accompanying figure, the X and Y coordinates (in meters) of station A are

1005.594 and 1868.720, respectively, and those of station B are 1564.865 and 644.491,

respectively. Angle BAP was measured as 308°56′39″ and angle ABP was measured as

58°53′30″. What are the coordinates of station P?

*11.13 In the accompanying figure, the X and Y coordinates (in feet) of station A are 1248.16

and 3133.35, respectively, and those of station B are 1509.15 and 1101.89, respectively.

The length of BP is 2657.45 ft, and the azimuth of line AP is

98 25 00 .

 



What are the

coordinates of station P?

11.14 In the accompanying figure, the X and Y coordinates (in feet) of station A are 1912.76

and 2238.63, respectively, and those of station B are 2342.39 and 1454.77, respectively.

The length of AP is 694.50 ft, and angle ABP is 43°10′44″? What are the possible

*11.15 A circle of radius 975.80 ft, centered at point A, intersects another circle of radius 963.09

ft, centered at point B. The X and Y coordinates (in feet) of A are 533.70 and 1157.86,

respectively, and those of B are 1142.93 and 269.83, respectively. What are the

coordinates of station P in the figure?

11.16 The same as Problem 11.15, except the radii from A and B are 837.45 ft and 1062.16 ft,

respectively.

11.17 For the subdivision in the accompanying figure, assume that lines AC, DF, GI, and JL

are parallel, but that lines BK and CL are parallel to each other, but not parallel to AJ. If

the X and Y coordinates (in feet) of station A are (5000.00, 5000.00), what are the

11.18 If the X and Y coordinates (in feet) of station A are (1000.00, 1000.00), what are the

coordinates of the remaining labeled corners in the accompanying figure?

Station

X

Y

Method

A

B

C

D

E

F

G

H

I

J

K

1000.00

1430.00

1235.58

1194.42

1215.00

1200.00

1230.00

1200.00

1230.00

1000.00

1400.01

1000.00

1193.82

1171.99

1146.01

1000.00

Given

Forward

Direction-Direction

Forward or Direction-Distance

Forward or Direction-Direction

Direction-Distance

Forward

*11.19 In Figure 11.8, the X and Y coordinates (in feet) of A are 616.31 and 1348.88,

respectively, those of B are 1261.68 and 1137.20, respectively, and those of C are

1852.83 and 1385.02, respectively. Also angle x is 27°08′55″ and angle y is 25°23′38″.

What are the coordinates of station P?

11.20 In Figure 11.8, the X and Y coordinates (in feet) of A are 2265.86 and 3008.76, those of

B are 2983.51 and 2802.25, and those of C are 3742.46 and 3026.83, respectively. Also

angle x is 28°00′18″ and angle y is 26°31′34″. What are the coordinates of station P?

11.21 In Figure 11.9, the following EN and XY coordinates for points A through C are given.

In a 2-D conformal coordinate transformation, to convert the XY coordinates into the EN

system, what are the

Point

E

N

X

Y

A

599,368.087

386,573.866

3639.18

2520.84

B

599,049.191

386,302.105

2444.05

1841.92

C

2622.15

2848.74

11.22 Do Problem 11.21 with the following coordinates.

State Plane Coordinates (m)

Arbitrary Coordinates (ft)

Point

E

N

X

Y

A

651,779.322

290,831.220

5504.32

3623.76

B

651,169.151

290,542.891

3409.59

2906.42

C

3849.59

3857.64

11.23 In Figure 11.12, the elevations of stations A and B are 210.05 ft, and 208.53 ft,

respectively. Instrument heights hiA and hiB are both 5.50 ft. What is the average

elevation of point P if the other field observations are:

11.24 In Problem 11.23, assume station P is to the left of the line AB, as viewed from station

A. If the X and Y coordinates (in feet) of station A are 2041.19 and 2938.76, respectively,

and the azimuth of line AB is 57°59′56″ what are the X and Y coordinates of the

inaccessible point?

11.25 In Figure 11.12, the elevations of stations A and B are 26.776 and 26.949 m, respectively.

AB = 112.531 m; A =57°52′55″; B = 62°13′08″; v1 = 32°18′39″’ v2 = 33°22′46″

Elev = 101.144 m

11.26 In Problem 11.25, assume station P is to the left of line AB as viewed from station A. If

the X and Y coordinates (in meters) of station A are 2985.465 and 3077.035, respectively,

and the azimuth of line AB is 125°32′15″ what are the X and Y coordinates of the

inaccessible point?

11.27 In Figure 11.13, the X, Y, and Z coordinates (in feet) of station A are 2897.37, 3406.73,

and 234.56, respectively, and those of B are 3126.27, 3394.46, and 241.69, respectively.

Determine the three-dimensional position of the occupied station P with the following

observations:

1

32 14 00 6.53ft 64 39 51

243.67 ft

   

     



A

v hr

PA

11.28 Adapt Equations (11.43) and (11.47) so they are applicable for zenith angles.

11.29 In Figure 11.13, the X, Y, and Z coordinates (in meters) of station A are 2634.100,

3119.530, and 252.796, respectively, and those of B are 2540.210, 3277.250, and

245.809, respectively. Determine the three-dimensional position of occupied station P

with the following observations:

1

69 26 06 2.000 m 57 51 53

179.439 m

   

     



A

z hr

PA

11.30 Use WOLFPACK to do Problem 11.9. (See solution to 11.9)

11.31 Use WOLFPACK to do Problem 11.10. (See solution to 11.10)

11.32 Use WOLFPACK to do Problem 11.12. (See solution to 11.12)

11.33 Use WOLFPACK to do Problem 11.13. (See solution to 11.13)

11.34 Use WOLFPACK to do Problem 11.15. (See solution to 11.15)

11.35 Use WOLFPACK to do Problem 11.16. (See solution to 11.16)

11.36 Use WOLFPACK to do Problem 11.17. (See solution to 11.17)