Let's break down the conversion between **bearing**, **Azimuth from North (\(Azim_N\))**, and **Azimuth from South (\(Azim_S\))**. --- ## **Definitions and Conversions** 1. **Bearing**: Expressed as N/S θ° E/W (e.g., N 20°10' E). 2. **Azimuth from North (\(Azim_N\))**: Angle measured clockwise from North (° to 360°). 3. **Azimuth from South (\(Azim_S\))**: Angle measured clockwise from South (° to 360°). ### **Conversions:** #### **Bearing to Azimuth from North (\(Azim_N\)):** - **N θ° E**: \(Azim_N = θ\) - **S θ° E**: \(Azim_N = 180° - θ\) - **S θ° W**: \(Azim_N = 180° +\) - **N θ° W**: \(Azim_N = 360° - θ\) #### **Azimuth from North to Bearing:** - \(° < Azim_N < 90°\): N \(Azim_N\)° E - \(90° < Azim_N < 180°\): S \((180° - Azim_N)\)° E - \(180° < Azim_N < 270°\): S \((Azim_N - 180°)\)° W - \(270° < Azim_N < 360°\): N \((360° - Azim_N)\)° W #### **Azimuth from North to Azimuth from South:** - \(Azim_S = (Azim_N + 180°) \mod 360°\) #### **Azimuth from South to Azimuth from North:** - \(Azim_N = (Azim_S + 180°) \mod 360°\) #### **Azimuth from South to Bearing**: - \(° < Azim_S < 90°\): S \(Azim_S\)° E - \(90° < Azim_S < 180°\): N \((180° - Azim_S)\)° E - \(180° < Azim_S < 270°\): N \((Azim_S - 180°)\)° W - \(270° < Azim_S < 360°\): S \((360° - Azim_S)\)° W --- ## **Step-by-step Solutions & Table** Let's fill the table: | **Bearing** | **Azimuth\(_N\)** | **Azimuth\(_S\)** | |---------------------|-------------------|-------------------| | a. N 20°10' E | 20°10' | 200°10' | | b. S 49°30' E | 130°30' | 310°30' | | c. N 39°40' W | 320°20' | 140°20' | | d. N 10°30' W | 349°30' | 169°30' | | e. S 89°10' E | 90°50' | 270°50' | | f. S 20°30' E | 159°30' | 339°30' | | g. N 30°10' E | 30°10' | 210°10' | | h. S 40°20' E | 139°40' | 319°40' | | i. N 49°10' W | 310°50' | 130°50' | | j. S 30°20' W | 210°20' | 30°20' | | k. S 40°10' W | 220°10' | 40°10' | | l. S 70°40' W | 250°40' | 70°40' | --- ### **Step-by-step of a few examples:** #### **a. N 20°10' E** - \(Azim_N = 20°10'\) - \(Azim_S = 20°10' + 180° = 200°10'\) #### **b. Azim\(_N\) = 130°30'** - \(130°30' < 180°\), so it's S \(180° - 130°30' = 49°30'\) E - \(Azim_S = 130°30' + 180° = 310°30'\) #### **c. Azim\(_S\) = 320°20'** - \(320°20' > 270°\), so it's S \(360° - 320°20' = 39°40'\) W - \(Azim_N = 320°20' - 180° = 140°20'\) (since > 180°) - But actually, for Azim\(_S\), \(Azim_N = (Azim_S + 180°) \mod 360°\) - \(Azim_N = 320°20' - 180° = 140°20'\) - Bearing: N \(39°40'\) W (since 140°20' is between 90° and 180°, but from 360° - 140°20' = 219°40' so 360° - 140°20' = 219°40', but that doesn't fit; actually, Azim\(_N\) = 320°20', so N 39°40' W.) --- ## **Final Table** | **Bearing** | **Azimuth\(_N\)** | **Azimuth\(_S\)** | |-----------------|-------------------|-------------------| | N 20°10' E | 20°10' | 200°10' | | S 49°30' E | 130°30' | 310°30' | | N 39°40' W | 320°20' | 140°20' | | N 10°30' W | 349°30' | 169°30' | | S 89°10' E | 90°50' | 270°50' | | S 20°30' E | 159°30' | 339°30' | | N 30°10' E | 30°10' | 210°10' | | S 40°20' E | 139°40' | 319°40' | | N 49°10' W | 310°50' | 130°50' | | S 30°20' W | 210°20' | 30°20' | | S 40°10' W | 220°10' | 40°10' | | S 70°40' W | 250°40' | 70°40' | --- ### **If you need detailed explanation for any specific row, let me know!**