A five-sided closed field traverse has the following distances in meters: AB = 51.766; BC = 26.947; CD = 37.070; DE = 35.292; EA = 19.192. The adjusted angles are as follows: A = 101°03′19″; B = 101°41′49″; C = 102°22′03″; D = 115°57′20″; E = 118°55′29″. The bearing of AB is N 73°00′00″ E. BC is in the S.E. quadrant.The coordinates of the five(5) corners of the traverse have been computed to be as follows: Corner "A" X Coordinate 1000.000 Y Coordinate 1000.000 Corner "B" X Coordinate 1050.019 Y Coordinate 1013.314 Corner "C" X Coordinate 1062.085 Y Coordinate 989.218 Corner "D" X Coordinate 1033.262 Y Coordinate 965.900 Corner "E" X Coordinate 1001.292 Y Coordinate 980.852 The area of the traverse using the coordinate method is 1,857 Square meters. If you used the area computation method we used in class and on the homeworks, the computed number using coordinate method for area computation for corner "C" is_______? Your answer will be in square meters to four (4) decimal place accuracy. |
In Co-ordinate method of area computation, we first write the Y co-ordinates and X co-ordinates as follows:-
Computations are done as under:
P = product along dashed line:
B : 1000 * 1013.314 = 1013314
C : 1050.019 * 989.218 = 1038697.695
D : 1062.085 * 965.900 = 1025867.902
E : 1033.262 * 980.852 = 1013477.099
A : 1001.292 * 1000 = 1011292
Q = Product along solid line:
B : 1000 * 1050.019 = 1050019
C : 1013.314 * 1062.085 = 1076225.6
D : 989.218 * 1033.262 = 1022121.369
E : 965.900 * 1001.292 = 96147.9428
A : 980.852 * 1000 = 980852
Computed Number at corners: P-Q
B : 1013314-10550019 = -36705
C : 1038697.695-1076225.6=-37527.905
D : 1025867.902-1022121.369=3746.33
E : 1013477.099-96147.9428=46329.1562
A : 1011292-980852=20440
Once computed numbers are calculated, we take there sum:
Sum = -36705-37527.905+3746.33+46329.1562+20440= -3717.4188
We then take the absolute value of the sum = abs(-3717.4188) = 3717.4188
The area will be half the value of the absolute sum = 3717.4188/2 = 1858.71 sq. meter
Given area = 1857. Hence, our computed area is very close to given value.
The question asks for the computed number at C which is -37527.905. The computed number to be reported in square meters is 37527.905 sq. meters.
A five-sided closed field traverse has the following distances in meters: AB = 51.766; BC = 26.94...
A five-sided closed field traverse has the following distances in meters: AB = 51.766; BC = 26.947; CD = 37.070; DE = 35.292; EA = 19.192. The adjusted angles are as follows: A = 101°03′19″; B = 101°41′49″; C = 102°22′03″; D = 115°57′20″; E = 118°55′29″. The bearing of AB is N 73°00′00″ E. BC is in the S.E. quadrant.The coordinates of the five(5) corners of the traverse have been computed to be as follows: Corner "A" X Coordinate...
Question 5 The four-sided, closed traverse has the following angles and distances: Az. 306 31 A 38° 30 B 100 38' C 149° 50 D 85° 59 E 165 03 AB 371.006 m BC 110.222 m CD 139.872 m AB 103.119 m AB 319.860 m Side AB has an azimuth of 306 31' (a) Perform the angle check and correct internal angles as needed. (b) Compute both bearings and azimuths for all sides (c) Compute the latitudes and departures for...
solve #6 1. Balance the following interior angles (angles to the right) of five sided closed polygon traverse. If the azimuth of side AB is fixed at 218 59 30, calculate the azimuths of the remaining sides. A-132°47 06, B-108"46 18, C= 107。19 37, D-81.50 36. E-109.16 18, (Note: Line BC bears SE) Compute departure and latitudes, linear misclosure and relative precision for the traverse of problem above, if the length of the side (in feet) are as follows: AB...
2. A closed traverse has the folowing data: LINES AB BC 1 BEARING N 30°30'E N 75° 30' W S 45°30' W DISTANCES 56.50 m 47.80 m CD 85.70 m DA eos Find the length of the ine DA 78.73 m b. 73.78 m 67.22 m 63.91 m Find the bearing of the line DA S 82057 E S 75° 26' E S 890 35 E S 62° 15 E Find the area of the traverse 3982.06 m2 b. 3680.33...
Consider a polygon traverse. The azimuth of side ABAB is fixed at 35∘09′32′′35∘09′32″. A=57∘00′50′′A=57∘00′50″, B=88∘24′45′′B=88∘24′45″, C=126∘36′58′′C=126∘36′58″, D=46∘03′25′′D=46∘03′25″, E=221∘53′52′′E=221∘53′52″. (Note: Line BCBC bears NW.) The lengths of the sides (in meters) are as follows: AB=383.808AB=383.808, BC=360.209BC=360.209, CD=342.204CD=342.204, DE=336.210DE=336.210, and EA=267.527EA=267.527. The coordinates of station AA are X=310,630.892mX=310,630.892m and Y=121,311.411mY=121,311.411m.
A)Compute the area between a lake and a straight line AG, from which offsets are taken at irregular intervals as shown in the table above (all distances in feet). Circle and express your answer to four significant figures and include appropriate units. PARTB A) Consider a polygon traverse. The azimuth of side AB is fixed at 35∘09′32′′. A=57∘00′50′′, B=88∘24′45′′, C=126∘36′58′′, D=46∘03′25′′,E=221∘53′52′′. (Note: Line BC bears NW.) The lengths of the sides (in meters) are as follows: AB=383.808, BC=360.209, CD=342.204, DE=336.210,and...
1)During a mountain climbing trip it is observed that the water used to cook a meal boils at 93 °C rather than the standard 100 °C at sea level. At what altitude are the climbers preparing their meal? (See Physical Properties of Water (SI Units) and Properties of the U.S. Standard Atmosphere (SI Units) for data needed to solve this 2)The following bearings taken on a closed compass and fill up the table. Lines Bearings (deg-min) Azimuth N Deflection Angles...
1) An observer fails to check the bubble of a level and it is off two divisions on a 100-m sight. If the sensitivity of the bubble is 20-sec, what error would there be in the reading? 2 ) The following azimuths are from the north: 329°20’, 180°35’, 48°32’, 170°30’, 145°25’, 319°35’, 350°45’, 95°49’, 11°30’, 235°45’. Express these directions as (a) azimuth from the south, (b) back azimuths, (c) bearings. 8) 6.7 The following azimuths are reckoned from the north:...
1) An observer fails to check the bubble of a level and it is off two divisions on a 100-m sight. If the sensitivity of the bubble is 20-sec, what error would there be in the reading? 2 ) The following azimuths are from the north: 329°20’, 180°35’, 48°32’, 170°30’, 145°25’, 319°35’, 350°45’, 95°49’, 11°30’, 235°45’. Express these directions as (a) azimuth from the south, (b) back azimuths, (c) bearings. 8) 6.7 The following azimuths are reckoned from the north:...
tively. If this area is to be leveled at RL-00 m 40) a (112,3, 78.42,5S.21. 32.81. 18.74) m compute the volume of earthwork 10 2 5.5 Problems L. The following are the balanced latitudes & departures 2+55.21+3281)+18.74)-2319.6 m t,...。s e departures for polygon ABCDEA . Compute the total area by coordinates met nates method, if Side Latitude Departme 156.16 coordinate of point A (100, 100y in meters. . Ifthis polygon drawn on map with scale 5 cm-251-BC m. Compute the...