# Calculating Bearings of Traverse Lines ## Given - The polygon is traversed in the order \( A \rightarrow B \rightarrow C \rightarrow D \rightarrow E \rightarrow F \rightarrow A \). - The **bearing of AB is \( N41^\circ 55'E \)**. - Interior angles to the right at each vertex are given. ## Step-by-Step Solution ### 1. **List the Angles to the Right** | At Vertex | Angle (to the right) | |-----------|----------------------| | A | 115° 10' | | B | 129° 11' | | C | 88° 35' | | D | 132° 30' | | E | 135° 42' | | F | 118° 52' | ### 2. **Traverse Bearings Calculation** Let’s define the bearings as follows: - Bearing of AB = θ₁ = \( N41^\circ 55'E \) - Bearing of BC = θ₂ - Bearing of CD = θ₃ - Bearing of DE = θ₄ - Bearing of EF = θ₅ - Bearing of FA = θ₆ #### **General Rule** The bearing of the next line = Previous bearing + (180° - angle to the right at the next station) Bearings are always measured clockwise from North. Always keep the bearing within °–360° by adding or subtracting 360° as necessary. --- #### **Step by Step Calculation** ##### **1. AB** - Given: θ₁ = 41° 55′ ##### **2. BC** - θ₂ = θ₁ + (180° - angle at B) - θ₂ = 41° 55′ + (180° - 129° 11′) - θ₂ = 41° 55′ + 50° 49′ = **92° 44′** ##### **3. CD** - θ₃ = θ₂ + (180° - angle at C) - θ₃ = 92° 44′ + (180° - 88° 35′) - θ₃ = 92° 44′ + 91° 25′ = **184° 09′** ##### **4. DE** - θ₄ = θ₃ + (180° - angle at D) - θ₄ = 184° 09′ + (180° - 132° 30′) - θ₄ = 184° 09′ + 47° 30′ = **231° 39′** ##### **5. EF** - θ₅ = θ₄ + (180° - angle at E) - θ₅ = 231° 39′ + (180° - 135° 42′) - θ₅ = 231° 39′ + 44° 18′ = **275° 57′** ##### **6. FA** - θ₆ = θ₅ + (180° - angle at F) - θ₆ = 275° 57′ + (180° - 118° 52′) - θ₆ = 275° 57′ + 61° 08′ = **337° 05′** --- ## 3. **Summary Table** | Line | Bearing (Azimuth from North) | |------|-------------------------------| | AB | 41° 55′ | | BC | 92° 44′ | | CD | 184° 09′ | | DE | 231° 39′ | | EF | 275° 57′ | | FA | 337° 05′ | --- ## 4. **Convert to Quadrantal Bearings (Optional)** - **AB:** N 41° 55′ E - **BC:** S 87° 16′ E (since 92° 44′ = 90° + 2° 44′, so S 2° 44′ E) - **CD:** S 4° 09′ W - **DE:** S 48° 21′ W - **EF:** S 84° 03′ W - **FA:** N 22° 55′ W (360° - 337° 05′ = 22° 55′) --- ## 5. **Final Bearings Table** | Line | Azimuth Bearing | Quadrantal Bearing | |------|-----------------|-------------------| | AB | 41° 55′ | N 41° 55′ E | | BC | 92° 44′ | S 2° 44′ E | | CD | 184° 09′ | S 4° 09′ W | | DE | 231° 39′ | S 48° 21′ W | | EF | 275° 57′ | S 84° 03′ W | | FA | 337° 05′ | N 22° 55′ W | --- **If you need detailed conversion or another format, let me know!**

# Correcting Bearings of Traverse Lines ## Given Information - **Starting Bearing:** \( N41^\circ 55'E \) for line AB. - **Interior Angles (to the right) at Each Vertex:** - A: 115° 10' - B: 129° 11' - C: 88° 35' - D: 132° 30' - E: 135° 42' - F: 118° 52' ## Traverse Order The polygon is traversed in the following order: 1. A → B 2. B → C 3. C → D 4. D → E 5. E → F 6. F → A ## Step-by-Step Calculation of Bearings ### 1. **AB** - **Bearing of AB:** \[ \theta_1 = 41^\circ 55' \] ### 2. **BC** - **Calculation for BC:** \[ \theta_2 = \theta_1 + (180^\circ - 129^\circ 11') \] \[ \theta_2 = 41^\circ 55' + 50^\circ 49' = 92^\circ 44' \] ### 3. **CD** - **Calculation for CD:** \[ \theta_3 = \theta_2 + (180^\circ - 88^\circ 35') \] \[ \theta_3 = 92^\circ 44' + 91^\circ 25' = 184^\circ 09' \] ### 4. **DE** - **Calculation for DE:** \[ \theta_4 = \theta_3 + (180^\circ - 132^\circ 30') \] \[ \theta_4 = 184^\circ 09' + 47^\circ 30' = 231^\circ 39' \] ### 5. **EF** - **Calculation for EF:** \[ \theta_5 = \theta_4 + (180^\circ - 135^\circ 42') \] \[ \theta_5 = 231^\circ 39' + 44^\circ 18' = 275^\circ 57' \] ### 6. **FA** - **Calculation for FA:** \[ \theta_6 = \theta_5 + (180^\circ - 118^\circ 52') \] \[ \theta_6 = 275^\circ 57' + 61^\circ 08' = 337^\circ 05' \] ## Summary of Bearings | Line | Bearing (Azimuth) | |------|--------------------| | AB | 41° 55' | | BC | 92° 44' | | CD | 184° 09' | | DE | 231° 39' | | EF | 275° 57' | | FA | 337° 05' | ## Quadrantal Bearings | Line | Quadrantal Bearing | |------|---------------------| | AB | N 41° 55' E | | BC | S 2° 44' E | | CD | S 4° 09' W | | DE | S 48° 21' W | | EF | S 84° 03' W | | FA | N 22° 55' W | This summary provides the corrected calculations for the bearings of the traverse lines based on the provided angles to the right. If further clarification or adjustments are needed, please let me know.