--- title: "Two point resection method" subject: "Surveying II" chapter: 5 key: "semester_4/surveying_ii:two-point-resection-method-describe" source: https://www.bctengineer.com/q/semester_4/surveying_ii/two-point-resection-method-describe site: BCT Engineering --- # Two point resection method Surveying II · Chapter 5: Orientation - Asked in: 2075 Bhadra, 6 marks - Video: [Two Point Problem| Surveying|Devesh Saini](https://www.youtube.com/watch?v=UpUnqyfF3u0) — Civil Beats - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/surveying_ii/two-point-resection-method-describe - Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-5 ## Question What is two point resection? Describe the two point resection method for finding the coordinates of unknown resection point. ## Short answer Two-point resection (Hansen’s problem) determines two unknown stations C and D from two known points A and B by observing angles at C and D. In quadrilateral ADCB, solve for ∠DAB using tangent formula: tan x = (sin P0 – K sin S)/(cos P0 – K cos S) with K and P0 from observed angles. Then compute distances and bearings to get coordinates of C and D. ## Answer **Two-point resection** is the method of finding the coordinates of two unknown stations C and D, from which two stations A and B of known coordinates are visible, by observing the horizontal angles at C and D. It is used when only two known points are available (Hansen's problem). **Problem:** Two known stations A and B are visible from two unknown stations C and D, which can also see each other. The angles $\angle ACB$ and $\angle DCA$ are observed at C, and $\angle ADB$ and $\angle BDC$ at D. Find the coordinates of C and D. ```text A _________________ B \ \ / \ \ / D ------ C ``` **Steps** 1. From the coordinates find $c = AB$ and the bearing of AB. 2. In the quadrilateral $A\,D\,C\,B$ the interior angles at the two observed stations are $\angle ADC = \angle ADB + \angle BDC$ and $\angle DCB = \angle ACB + \angle DCA$. 3. Let $x = \angle DAB$ and $y = \angle CBA$. Their sum is $S = x + y = 360^\circ - \angle ADC - \angle DCB$. 4. From triangle ABD: $AD = \dfrac{c\sin p}{\sin\angle ADB}$ with $p = \angle ABD = 180^\circ - \angle ADB - x$. From triangle ABC: $AC = \dfrac{c\sin y}{\sin\angle ACB}$. 5. In triangle ADC: $\dfrac{AD}{\sin\angle DCA} = \dfrac{AC}{\sin\angle ADC}$. Combining, $$ \sin(P_0 - x) = K\sin(S - x), \qquad K = \frac{\sin\angle ADB\,\sin\angle DCA}{\sin\angle ACB\,\sin\angle ADC}, \quad P_0 = 180^\circ - \angle ADB $$ which gives $$ \tan x = \frac{\sin P_0 - K\sin S}{\cos P_0 - K\cos S} $$ 6. With $x$ known, find $y = S - x$, then $AD$, $BC$ (from triangle ABC: $BC = \dfrac{c\sin q}{\sin\angle ACB}$, $q = 180^\circ - \angle ACB - y$). 7. Bearing of $AD$ = bearing of $AB \pm x$; bearing of $BC$ = bearing of $BA \mp y$ (according to the side of AB on which C and D lie). Then $E = E_A + AD\sin\theta,\; N = N_A + AD\cos\theta$, and similarly for C from B. 8. Check: the distance CD computed from the coordinates must agree with the distance found from triangle ADC. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is two-point resection (Hansen's problem)? A. Finding C and D, two unknown stations that see each other, by observing angles at them to two known stations A and B B. Finding one unknown station by observing three known stations C. Finding the length AB from two angles D. Setting out two points from a baseline by chaining Answer: A. Two unknown stations C and D, from which known A and B are visible, are fixed by horizontal angles observed at C and D. (Key point: Definition of two-point resection) 2. In quadrilateral ADCB with x = ∠DAB and y = ∠CBA, what is S = x + y? A. S = 180° - ∠ADC - ∠DCB B. S = ∠ADC + ∠DCB - 180° C. S = 360° - ∠ADC - ∠DCB D. S = 360° - ∠ADB - ∠ACB Answer: C. Angles of the quadrilateral sum to 360°, so x + y = 360° - ∠ADC - ∠DCB. (Key point: Sum of x and y) 3. What does combining the sine rule in triangles ABD, ABC and ADC lead to? A. sin(P0 - x) = K sin(S - x), so tan x = (sin P0 - K sin S)/(cos P0 - K cos S) B. sin(P0 + x) = K cos(S + x) C. tan x = K sin S D. cos x = K cos S Answer: A. AD is found from triangle ABD and AC from triangle ABC; the sine rule in ADC then gives sin(P0 - x) = K sin(S - x) with K = sin∠ADB sin∠DCA / (sin∠ACB sin∠ADC). (Key point: Key equation for x) 4. How is the work checked at the end? A. Sum of x and y must equal 180° B. AD must equal BC C. AB must equal CD D. The distance CD from coordinates must agree with that from triangle ADC Answer: D. CD computed from the final coordinates of C and D must match the CD found from triangle ADC. (Key point: Check on result) ## Related in Surveying II - [Resection, two point problem, intersection](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-two-point-problem-ab-p) — Surveying II, chapter 5 - [Three point analytical resection, average coordinates of O](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Athree-point-resection-p-w-d) — Surveying II, chapter 5 - [Two point resection, point C from A, B, D](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atwo-point-resection-acb-dca-adb) — Surveying II, chapter 5 - [Two point resection, point C (A, B at 7928.474 N)](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atwo-point-resection-c-a-b) — Surveying II, chapter 5 - [Intersection vs resection, three point method](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aintersection-vs-resection-three-point) — Surveying II, chapter 5 - [Resection point P from L, M, N](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-lmn-p-2079j) — Surveying II, chapter 5 ## Related in other subjects - [Two-point resection in plane tabling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-point-resection-plane-table) — Surveying I, chapter 6 - [Resection by three point problem](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Athree-point-resection-sketches) — Surveying I, chapter 6 - [Area coordinates and temperature at a point](https://www.bctengineer.com/question.md?key=semester_8%2Ffinite_element_method%3Acst-area-coordinates-interpolation) — Finite Element Method, chapter 5 - [Two point problem; advantages, disadvantages](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-point-problem-adv-disadv) — Surveying I, chapter 6