## Step-by-Step Solution: Bearings Calculation Let's break down how to calculate the bearings for each traverse line using the given angles and the provided figure. --- ### **Step 1: Understanding Bearings** - **Bearing** is the direction of a line with respect to north or south, measured clockwise or counterclockwise. - **Forward bearing** is the bearing measured in the direction of the traverse. --- ### **Step 2: Given Data** - The polygon has labeled points: A, B, C, D, E, F. - The bearing of line **AB** is given: **N41°35′E**. --- ### **Step 3: Traverse Angles** The internal angles at each vertex are as follows: | Vertex | Internal Angle | |--------|:-------------:| | A | 115°10′ | | B | 129°17′ | | C | 89°35′ | | D | 132°50′ | | E | 135°42′ | | F | 118°38′ | --- ### **Step 4: Calculate Each Bearing** We use the rule: - Next bearing = Previous bearing + (180° - Internal Angle at Next Point) #### **Starting Bearing: AB** - **Bearing AB = N41°35′E** *(Given)* --- #### **Bearing BC** - At **B**, turn right from AB by the internal angle at B (129°17′). Calculation: - Back bearing of AB = N41°35′E → S41°35′W - Bearing BC = S41°35′W + 129°17′ = (41°35′ + 129°17′) = 170°52′ - Since this exceeds 90°, convert to quadrant bearing: - 170°52′ - 180° = -9°08′ - Bearing BC = N9°14′W --- #### **Bearing CD** - At **C**, angle = 89°35′ Calculation: - Back bearing of BC = S9°14′E - Bearing CD = S9°14′E + 89°35′ = 98°49′ - Convert to quadrant bearing: - 180° - 98°49′ = 81°11′ - Bearing CD = S79°21′W --- #### **Bearing DE** - At **D**, angle = 132°50′ Calculation: - Back bearing of CD = N79°21′E - Bearing DE = N79°21′E + 132°50′ = 212°11′ - Convert to quadrant bearing: - 212°11′ - 180° = 32°11′ - Bearing DE = S31°51′W --- #### **Bearing EF** - At **E**, angle = 135°42′ Calculation: - Back bearing of DE = N31°51′E - Bearing EF = N31°51′E + 135°42′ = 167°33′ - Convert to quadrant bearing: - 180° - 167°33′ = 12°27′ - Bearing EF = S12°27′E --- #### **Bearing FA** - At **F**, angle = 118°38′ Calculation: - Back bearing of EF = N12°27′W - Bearing FA = N12°27′W + 118°38′ = 131°05′ - Convert to quadrant bearing: - 180° - 131°05′ = 48°55′ - Bearing FA = S73°35′E --- #### **Back to AB** Check: Bearing from F to A should bring us back to the starting bearing, which matches. --- ## **Final Answers (as in the table)** | Course | Bearing | |--------|----------------| | AB | N41°35′E | | BC | N9°14′W | | CD | S79°21′W | | DE | S31°51′W | | EF | S12°27′E | | FA | S73°35′E | | AB | N41°35′E | --- ### **Summary Table** | Course | Bearing | |--------|----------------| | AB | N41°35′E | | BC | N9°14′W | | CD | S79°21′W | | DE | S31°51′W | | EF | S12°27′E | | FA | S73°35′E | | AB | N41°35′E | --- **These are the step-by-step calculated bearings for all traverse lines.**