VIPSolutions

VIPSolutions logo ✨ VIPSolutions

Home Dashboard Ask AI Archive

The calculated bearings for all traverse lines of the polygon are summarized in the table below. The calculations proceed sequentially, starting with the given bearing of line AB and using the measured interior angle at each station. Summary of Traverse Bearings | Traverse Line | Bearing (Forward Bearing) | |---|---| | AB | \mathbf{N \ 41^\circ 35' \ E} (Given) | | BC | \mathbf{N \ 9^\circ 14' \ W} | | CD | \mathbf{S \ 79^\circ 21' \ W} | | DE | \mathbf{S \ 31^\circ 51' \ W} | | EF | \mathbf{S \ 12^\circ 27' \ E} | | FA | \mathbf{S \ 73^\circ 35' \ E} | Detailed Calculation Steps The bearing of the next line is found by: \text{Bearing}_{\text{Next Line}} = \text{Back Bearing}_{\text{Previous Line}} \pm \text{Interior Angle} We use Whole Circle Bearings (WCB) for easy calculation, where \text{WCB} = \text{Quadrant Bearing (QB)} for N/E lines, \text{WCB} = 180^\circ - \text{QB} for S/E lines, etc. The Back Bearing (BB) is always \text{FB} \pm 180^\circ. Since the angles are interior and measured to the right (clockwise) from the back line, we use: \text{WCB}_{\text{Next}} = \text{WCB}_{\text{Back Line}} + \text{Interior Angle} 1. Line AB \to BC * Given \text{FB}_{AB}: \mathbf{N \ 41^\circ 35' \ E} (\text{WCB}_{AB} = 41^\circ 35') * Back Bearing \text{BB}_{AB} at B (\text{WCB}_{BA}): 41^\circ 35' + 180^\circ 00' = 221^\circ 35' * Angle \angle B: 129^\circ 11' * \text{WCB}_{BC}: 221^\circ 35' + 129^\circ 11' = 350^\circ 46' * \text{FB}_{BC} (QB): 360^\circ 00' - 350^\circ 46' = 9^\circ 14' \implies \mathbf{N \ 9^\circ 14' \ W} 2. Line BC \to CD * \text{FB}_{BC}: \mathbf{N \ 9^\circ 14' \ W} * Back Bearing \text{BB}_{BC} at C (\text{WCB}_{CB}): 360^\circ 00' - 9^\circ 14' = 350^\circ 46', then 350^\circ 46' - 180^\circ 00' = 170^\circ 46' * Angle \angle C: 88^\circ 35' * \text{WCB}_{CD}: 170^\circ 46' + 88^\circ 35' = 259^\circ 21' * \text{FB}_{CD} (QB): 259^\circ 21' - 180^\circ 00' = 79^\circ 21' \implies \mathbf{S \ 79^\circ 21' \ W} 3. Line CD \to DE * \text{FB}_{CD}: \mathbf{S \ 79^\circ 21' \ W} * Back Bearing \text{BB}_{CD} at D (\text{WCB}_{DC}): 259^\circ 21' - 180^\circ 00' = 79^\circ 21' * Angle \angle D: 132^\circ 30' * \text{WCB}_{DE}: 79^\circ 21' + 132^\circ 30' = 211^\circ 51' * \text{FB}_{DE} (QB): 211^\circ 51' - 180^\circ 00' = 31^\circ 51' \implies \mathbf{S \ 31^\circ 51' \ W} 4. Line DE \to EF * \text{FB}_{DE}: \mathbf{S \ 31^\circ 51' \ W} * Back Bearing \text{BB}_{DE} at E (\text{WCB}_{ED}): 211^\circ 51' - 180^\circ 00' = 31^\circ 51' * Angle \angle E: 135^\circ 42' * \text{WCB}_{EF}: 31^\circ 51' + 135^\circ 42' = 167^\circ 33' * \text{FB}_{EF} (QB): 180^\circ 00' - 167^\circ 33' = 12^\circ 27' \implies \mathbf{S \ 12^\circ 27' \ E} 5. Line EF \to FA * \text{FB}_{EF}: \mathbf{S \ 12^\circ 27' \ E} * Back Bearing \text{BB}_{EF} at F (\text{WCB}_{FE}): 167^\circ 33' + 180^\circ 00' = 347^\circ 33' * Angle \angle F: 118^\circ 52' * \text{WCB}_{FA}: 347^\circ 33' + 118^\circ 52' = 466^\circ 25' * 466^\circ 25' - 360^\circ 00' = 106^\circ 25' * \text{FB}_{FA} (QB): 180^\circ 00' - 106^\circ 25' = 73^\circ 35' \implies \mathbf{S \ 73^\circ 35' \ E} 6. Line FA \to AB (Closure Check) * \text{FB}_{FA}: \mathbf{S \ 73^\circ 35' \ E} * Back Bearing \text{BB}_{FA} at A (\text{WCB}_{AF}): 106^\circ 25' + 180^\circ 00' = 286^\circ 25' * Angle \angle A: 115^\circ 10' * Calculated \text{WCB}_{AB}: 286^\circ 25' + 115^\circ 10' = 401^\circ 35' * 401^\circ 35' - 360^\circ 00' = 41^\circ 35' * Calculated \text{FB}_{AB} (QB): 41^\circ 35' \implies \mathbf{N \ 41^\circ 35' \ E} * The calculated bearing matches the given bearing, confirming the accuracy of the calculations.

Question:

The calculated bearings for all traverse lines of the polygon are summarized in the table below. The calculations proceed sequentially, starting with the given bearing of line AB and using the measured interior angle at each station. Summary of Traverse Bearings | Traverse Line | Bearing (Forward Bearing) | |---|---| | AB | \mathbf{N \ 41^\circ 35' \ E} (Given) | | BC | \mathbf{N \ 9^\circ 14' \ W} | | CD | \mathbf{S \ 79^\circ 21' \ W} | | DE | \mathbf{S \ 31^\circ 51' \ W} | | EF | \mathbf{S \ 12^\circ 27' \ E} | | FA | \mathbf{S \ 73^\circ 35' \ E} | Detailed Calculation Steps The bearing of the next line is found by: \text{Bearing}_{\text{Next Line}} = \text{Back Bearing}_{\text{Previous Line}} \pm \text{Interior Angle} We use Whole Circle Bearings (WCB) for easy calculation, where \text{WCB} = \text{Quadrant Bearing (QB)} for N/E lines, \text{WCB} = 180^\circ - \text{QB} for S/E lines, etc. The Back Bearing (BB) is always \text{FB} \pm 180^\circ. Since the angles are interior and measured to the right (clockwise) from the back line, we use: \text{WCB}_{\text{Next}} = \text{WCB}_{\text{Back Line}} + \text{Interior Angle} 1. Line AB \to BC * Given \text{FB}_{AB}: \mathbf{N \ 41^\circ 35' \ E} (\text{WCB}_{AB} = 41^\circ 35') * Back Bearing \text{BB}_{AB} at B (\text{WCB}_{BA}): 41^\circ 35' + 180^\circ 00' = 221^\circ 35' * Angle \angle B: 129^\circ 11' * \text{WCB}_{BC}: 221^\circ 35' + 129^\circ 11' = 350^\circ 46' * \text{FB}_{BC} (QB): 360^\circ 00' - 350^\circ 46' = 9^\circ 14' \implies \mathbf{N \ 9^\circ 14' \ W} 2. Line BC \to CD * \text{FB}_{BC}: \mathbf{N \ 9^\circ 14' \ W} * Back Bearing \text{BB}_{BC} at C (\text{WCB}_{CB}): 360^\circ 00' - 9^\circ 14' = 350^\circ 46', then 350^\circ 46' - 180^\circ 00' = 170^\circ 46' * Angle \angle C: 88^\circ 35' * \text{WCB}_{CD}: 170^\circ 46' + 88^\circ 35' = 259^\circ 21' * \text{FB}_{CD} (QB): 259^\circ 21' - 180^\circ 00' = 79^\circ 21' \implies \mathbf{S \ 79^\circ 21' \ W} 3. Line CD \to DE * \text{FB}_{CD}: \mathbf{S \ 79^\circ 21' \ W} * Back Bearing \text{BB}_{CD} at D (\text{WCB}_{DC}): 259^\circ 21' - 180^\circ 00' = 79^\circ 21' * Angle \angle D: 132^\circ 30' * \text{WCB}_{DE}: 79^\circ 21' + 132^\circ 30' = 211^\circ 51' * \text{FB}_{DE} (QB): 211^\circ 51' - 180^\circ 00' = 31^\circ 51' \implies \mathbf{S \ 31^\circ 51' \ W} 4. Line DE \to EF * \text{FB}_{DE}: \mathbf{S \ 31^\circ 51' \ W} * Back Bearing \text{BB}_{DE} at E (\text{WCB}_{ED}): 211^\circ 51' - 180^\circ 00' = 31^\circ 51' * Angle \angle E: 135^\circ 42' * \text{WCB}_{EF}: 31^\circ 51' + 135^\circ 42' = 167^\circ 33' * \text{FB}_{EF} (QB): 180^\circ 00' - 167^\circ 33' = 12^\circ 27' \implies \mathbf{S \ 12^\circ 27' \ E} 5. Line EF \to FA * \text{FB}_{EF}: \mathbf{S \ 12^\circ 27' \ E} * Back Bearing \text{BB}_{EF} at F (\text{WCB}_{FE}): 167^\circ 33' + 180^\circ 00' = 347^\circ 33' * Angle \angle F: 118^\circ 52' * \text{WCB}_{FA}: 347^\circ 33' + 118^\circ 52' = 466^\circ 25' * 466^\circ 25' - 360^\circ 00' = 106^\circ 25' * \text{FB}_{FA} (QB): 180^\circ 00' - 106^\circ 25' = 73^\circ 35' \implies \mathbf{S \ 73^\circ 35' \ E} 6. Line FA \to AB (Closure Check) * \text{FB}_{FA}: \mathbf{S \ 73^\circ 35' \ E} * Back Bearing \text{BB}_{FA} at A (\text{WCB}_{AF}): 106^\circ 25' + 180^\circ 00' = 286^\circ 25' * Angle \angle A: 115^\circ 10' * Calculated \text{WCB}_{AB}: 286^\circ 25' + 115^\circ 10' = 401^\circ 35' * 401^\circ 35' - 360^\circ 00' = 41^\circ 35' * Calculated \text{FB}_{AB} (QB): 41^\circ 35' \implies \mathbf{N \ 41^\circ 35' \ E} * The calculated bearing matches the given bearing, confirming the accuracy of the calculations.

This is AI generated Response.
Asked by: VARRI NAVEEN
Created at: 2025-09-26 20:10:16

Final Answer:

Rendered Raw Text
Did you like this answer?
# Traverse Bearing Calculations This document summarizes the calculation of forward bearings for each side of a closed traverse using interior angles measured clockwise at each station. Whole Circle Bearings (WCB) are used for calculation convenience, with quadrant bearings (QB) shown in the summary. ## Bearing Calculation Formula For a traverse line, the forward bearing (\(\text{FB}\)) of the next line is calculated as: \[ \text{WCB}_{\text{Next}} = \text{WCB}_{\text{Back Line}} + \text{Interior Angle} \] where the **back bearing** is the forward bearing ± \(180^\circ\). Adjust the result to fall within \(^\circ\)–\(360^\circ\) as needed. ## Traverse Bearing Table | Traverse Line | Bearing (Forward Bearing) | |---------------|--------------------------| | AB | **N 41° 35' E** (Given) | | BC | **N 9° 14' W** | | CD | **S 79° 21' W** | | DE | **S 31° 51' W** | | EF | **S 12° 27' E** | | FA | **S 73° 35' E** | ## Step-by-Step Calculations ### 1. Line AB → BC - **Given**: \(\text{FB}_{AB} = N\ 41^\circ 35'\ E\) (\(\text{WCB}_{AB} = 41^\circ 35'\)) - **Back Bearing at B**: \(41^\circ 35' + 180^\circ = 221^\circ 35'\) - **Interior Angle at B**: \(129^\circ 11'\) - **WCB for BC**: \(221^\circ 35' + 129^\circ 11' = 350^\circ 46'\) - **QB for BC**: \(360^\circ - 350^\circ 46' = 9^\circ 14'\) **Bearing: N 9° 14' W** ### 2. Line BC → CD - **FB for BC**: \(N\ 9^\circ 14'\ W\) (\(\text{WCB}_{BC} = 350^\circ 46'\)) - **Back Bearing at C**: \(350^\circ 46' - 180^\circ = 170^\circ 46'\) - **Interior Angle at C**: \(88^\circ 35'\) - **WCB for CD**: \(170^\circ 46' + 88^\circ 35' = 259^\circ 21'\) - **QB for CD**: \(259^\circ 21' - 180^\circ = 79^\circ 21'\) **Bearing: S 79° 21' W** ### 3. Line CD → DE - **FB for CD**: \(S\ 79^\circ 21'\ W\) (\(\text{WCB}_{CD} = 259^\circ 21'\)) - **Back Bearing at D**: \(259^\circ 21' - 180^\circ = 79^\circ 21'\) - **Interior Angle at D**: \(132^\circ 30'\) - **WCB for DE**: \(79^\circ 21' + 132^\circ 30' = 211^\circ 51'\) - **QB for DE**: \(211^\circ 51' - 180^\circ = 31^\circ 51'\) **Bearing: S 31° 51' W** ### 4. Line DE → EF - **FB for DE**: \(S\ 31^\circ 51'\ W\) (\(\text{WCB}_{DE} = 211^\circ 51'\)) - **Back Bearing at E**: \(211^\circ 51' - 180^\circ = 31^\circ 51'\) - **Interior Angle at E**: \(135^\circ 42'\) - **WCB for EF**: \(31^\circ 51' + 135^\circ 42' = 167^\circ 33'\) - **QB for EF**: \(180^\circ - 167^\circ 33' = 12^\circ 27'\) **Bearing: S 12° 27' E** ### 5. Line EF → FA - **FB for EF**: \(S\ 12^\circ 27'\ E\) (\(\text{WCB}_{EF} = 167^\circ 33'\)) - **Back Bearing at F**: \(167^\circ 33' + 180^\circ = 347^\circ 33'\) - **Interior Angle at F**: \(118^\circ 52'\) - **WCB for FA**: \(347^\circ 33' + 118^\circ 52' = 466^\circ 25'\) - **Adjust**: \(466^\circ 25' - 360^\circ = 106^\circ 25'\) - **QB for FA**: \(180^\circ - 106^\circ 25' = 73^\circ 35'\) **Bearing: S 73° 35' E** ### 6. Closure Check (FA → AB) - **FB for FA**: \(S\ 73^\circ 35'\ E\) (\(\text{WCB}_{FA} = 106^\circ 25'\)) - **Back Bearing at A**: \(106^\circ 25' + 180^\circ = 286^\circ 25'\) - **Interior Angle at A**: \(115^\circ 10'\) - **WCB for AB**: \(286^\circ 25' + 115^\circ 10' = 401^\circ 35'\) - **Adjust**: \(401^\circ 35' - 360^\circ = 41^\circ 35'\) **Matches initial bearing: N 41° 35' E** ## Notes - All angles and bearings are expressed in degrees (°) and minutes ('). - The bearings are checked for closure; the final calculation matches the given starting bearing, verifying correctness. --- **Diagram illustration is recommended but not provided here.** *(If included, the diagram would show the traverse with labeled points and bearings. Alt text: "Closed traverse polygon with labeled points A-F and forward bearings on each side.")*

📢 Instructions:

  • Ask anything relatd to above question only.
  • For new Question goto :
    Ask AI

Related Answers

Study Help, Fast Answers

VIPSolutions focuses on clear, step‑by‑step explanations so you can learn quickly. Whether you need an AI‑generated walkthrough or a short hint to get unstuck, each solution is organized for fast reading and easy review later.

Search similar questions, compare approaches, and bookmark the best answers for revision. Our goal is simple: quick, reliable study help that feels natural—not noisy.