New Method of Getting Position of Instrument Station Based on Two Known Points and The Law of Cosines

Document Type : Regular Article


Lecturer, Department of Civil Engineering, Politeknik Negeri Balikpapan, Indonesia


Getting the position of the instrument in starting traverse and staking out surveying can be very helpful for the surveyors. The most common method is the placement of the instrument on the known point, then those surveys are possible to be accomplished. This research is aimed to develop a new method and procedure to get x, y, and z values of the unknown position of the instrument based on two known points and the law of cosines. The method of this research is the implementation of the law of cosines and Euclidean Norm in solving the problem of getting the coordinate of instrument position. The innovation of this procedure has not been used yet in survey practice and has not been accommodated in electronic distance measuring (EDM) based survey instruments such as Total Station. The experiment of measurement to test the procedure is conducted virtually using the total station of SimusurveyX 1.0.7. The total measurement of ten random triangles is 60 times, where each triangle is measured 6 times. The result of measurement is close to the ground truth, and it can be repeatable. The implication of this research is enabling the surveyors to shortcut traverse measurement by locating Total Station in the first unknown point of the traverse.


  • The power of the law of cosine in determining the position.
  • Determining unknown position using 2 known points on the earth’s surface.
  • Breakthrough for Traverse and Stake Out Surveying.
  • Opportunity in the development of the built-in app in survey instruments.


Main Subjects

[1]     Lin P-J, Huang Y-C, Huang Y-J, Ker M-D. Implementation of the cosine law for location awareness system. 2010 Asia Pacific Conf. Postgrad. Res. Microelectron. Electron., IEEE; 2010, p. 255–8.
[2]     Yangyang X, Kefeng Y, Yan Z, Ming C. Research of Indoor Localization Technology of Robot Based on Cosines Law. 2020 IEEE Int. Conf. Adv. Electr. Eng. Comput. Appl. AEECA), IEEE; 2020, p. 929–32.
[3]     Sulistyo T, Achmad K, Purnama IBI. The Asset Management and Tracking System for Technical and Vocational Education and Training (TVET) Institution Based on Ubiquitous Computing. ComTech Comput Math Eng Appl 2022;13:23–34.
[4]     Sulistyo T, Achmad K, Respati S. GeomatikaDroid: An Android application for improving theodolite measurement. J. Phys. Conf. Ser., vol. 1450, IOP Publishing; 2020, p. 12021.
[5]     Sulistyo T, Achmad K, Purnama IBI. Empowering Low-Cost Survey Instrument for the Stake-Out Measurements Using Android Application 2021.
[6]     Dib H, Adamo-Villani N. An e-tool for undergraduate surveying education: design and evaluation. ICST Trans e-Education e-Learning 2011;11:e5.
[7]     Singh R, Artman D, Taylor DW, Brinton D. Basic surveying-theory and practice. Rep. Present. Dur. Ninth Annu. Semin. Geom. by Oregon Dep. Transp. Unit. Bend, Oregon, 2000.
[9]     DiBiase D. Nature of Geographic Information: An Open Geospatial Textbook. Nat Geogr Inf An Open Geospatial Textb 2012.
[10]   Font-Llagunes JM, Batlle JA. New Method That Solves the Three-Point Resection Problem Using Straight Lines Intersection. J Surv Eng 2009;135:39–45.
[11]   Chandra AM. Surveying : problem solving with theory and objective type questions. New Age Int Ltd 2005.
[12]   Ghilani CD, R.Wolf P. Elementary surveying : an introduction to geomatics,. 13th ed. Prentice Hall, Bost. Mass, 2012.
[13]   International Organization for Standardization. Accuracy (trueness and precision) of measurement methods and results - DIN ISO 5725-2:2020. Int Organ Stand 2020:23.
[14]   Sulistyo T, Achmad K, Giarto RB. Geomatics Accuracy and Precision of Determination Horizontal Distances in Stake Out Measurement Using Theodolite. JUTEKS  J Tek Sipil 2019;4:74.
[15]   Kang SC, Chuang SK, Shiu RS, Chen Y, Hsieh SH. Simusurvey X: An improved virtual surveying instrument running off a game engine. EG-ICE 2010 - 17th Int. Work. Intell. Comput. Eng., 2019.
[16]   Aufmann RN, Barker VC, Nation RD. College trigonometry. Cengage Learning; 2007.
[17]   Deisenroth MP, Faisal AA, Ong CS. Mathematics for Machine Learning. Cambridge University Press; 2020.
[18]   Safaeian Hamzehkolaei N, Alizamir M. Performance Evaluation of Machine Learning Algorithms for Seismic Retrofit Cost Estimation Using Structural Parameters. J Soft Comput Civ Eng 2021;5:32–57.
[19]   Jain P, Ahuja L, Sharma A. Current state of the research in agile quality development. Proc. 10th INDIACom; 2016 3rd Int. Conf. Comput. Sustain. Glob. Dev. INDIACom 2016, 2016, p. 1177–9.
[20]   Mohammed SI. Important methods measurements to exam the accuracy and reliability of reflector-less total station measurements. J Phys Conf Ser 2021;1895:012007.
[21]   Kovačič B, Kamnik R, Pustovgar A, Vatin N. Analysis of Precision of Geodetic Instruments for Investigating Vertical Displacement of Structures. Procedia Eng 2016;165:906–17.