1. **Problem Statement:** You want to plot a polygon step-by-step using bearings and distances, converting bearings to coordinates, checking closure, and calculating area. 2. **Formula for Latitude and Departure:** Given a side length $L$ and bearing angle $\theta$, compute: $$\text{Latitude } (\Delta Y) = L \times \cos(\theta)$$ $$\text{Departure } (\Delta X) = L \times \sin(\theta)$$ Note: Adjust signs based on quadrant (N/S and E/W). 3. **Example Calculation:** For side AB = 189.53 m, bearing S 6°15' W ($\theta = 6.25^\circ$): $$\cos(6.25^\circ) = 0.9941 \Rightarrow \Delta Y = 189.53 \times 0.9941 = 188.41$$ $$\sin(6.25^\circ) = 0.1089 \Rightarrow \Delta X = 189.53 \times 0.1089 = 20.64$$ Since bearing is S-W, both $\Delta Y$ and $\Delta X$ are negative: $$\Delta Y = -188.41, \quad \Delta X = -20.64$$ 4. **Calculate Coordinates:** Start at Point A $(0,0)$. Point B: $$X_b = X_a + \Delta X = 0 - 20.64 = -20.64$$ $$Y_b = Y_a + \Delta Y = 0 - 188.41 = -188.41$$ Repeat for other points by adding their respective $\Delta X$ and $\Delta Y$. 5. **Traverse Closure Check:** Sum all $\Delta X$ and $\Delta Y$ for all sides: $$\sum \Delta X \approx 0, \quad \sum \Delta Y \approx 0$$ If sums are close to zero, the polygon is closed correctly. 6. **Calculate Diagonals:** Use distance formula between points, e.g., for diagonal AC: $$d = \sqrt{(X_c - X_a)^2 + (Y_c - Y_a)^2}$$ 7. **Divide Polygon into Triangles:** Example triangles: $\triangle ABC$, $\triangle ACD$, $\triangle ADE$. 8. **Compute Area Using Heron's Formula:** For triangle with sides $a,b,c$: $$s = \frac{a+b+c}{2}$$ $$A = \sqrt{s(s-a)(s-b)(s-c)}$$ Sum areas of all triangles for total polygon area. This step-by-step method helps you manually plot polygons from bearings and distances. If you want, I can also show the shortcut shoelace method next!