1. The problem involves analyzing a traverse survey with measured angles $\beta_i$, bearing angles $\alpha_i$, distances $S_i$, coordinate differences $\Delta Y_i$, $\Delta X_i$, and their uncertainties. 2. The key formulas are: - Bearing angle update: $$\alpha_{i,i+1} = \alpha_{i-1,i} + \beta_i + v_{\beta_i} \pm 200^g$$ - Coordinate differences: $$\Delta Y_i = S_i \sin \alpha_i$$ and $$\Delta X_i = S_i \cos \alpha_i$$ - Coordinate differences sum: $$Y_{end} - Y_{start} = \sum \Delta Y_i$$ and $$X_{end} - X_{start} = \sum \Delta X_i$$ - Misclosure in angles: $$f_\beta = \sum \beta_i - (\alpha^{end} - \alpha^{start} + n \times 200^g)$$ - Misclosure in coordinates: $$f_Y = (Y_{end} - Y_{start}) - \sum \Delta Y_i$$ and $$f_X = (X_{end} - X_{start}) - \sum \Delta X_i$$ - Adjusted uncertainties: $$v_Y = -\frac{f_Y}{[S]} S$$ and $$v_X = -\frac{f_X}{[S]} S$$ where $[S]$ is total traverse length. 3. From the data, the sums are: - Sum of measured angles $\sum \beta_i = 1303.837^g$ - Sum of distances $\sum S_i = 1190.811$ m - Sum of coordinate differences $\sum \Delta Y_i = 814.0255$ m, $\sum \Delta X_i = 273.20476$ m - Coordinate differences uncertainties sum $\sum v_{\Delta Y} = 88.80156$ mm 4. The misclosure in angles $f_\beta$ is given as $-0.0095^g$. 5. The total traverse length $[S] = 1190.811$ m. 6. Using the formulas, the coordinate misclosures $f_Y$ and $f_X$ can be computed from the difference between end and start coordinates minus sums of $\Delta Y_i$ and $\Delta X_i$ respectively. 7. The adjusted uncertainties $v_Y$ and $v_X$ are proportional to the misclosures and distances. 8. The final adjusted uncertainties and misclosures help in correcting the traverse measurements for accuracy. This completes the analysis of the first problem regarding the traverse survey data and its angle and coordinate computations.