Answer:

The relative precision of a traverse is a measure of how well the observed measurements fit the mathematical model of the traverse. It is defined as the ratio of the closing error to the total length of the traverse.

Given:
Total length of the traverse = 500 m
Closing error = 0.289 m

To find the relative precision, we divide the closing error by the total length of the traverse:

Relative precision = Closing error / Total length of traverse

Substituting the given values, we have:

Relative precision = 0.289 m / 500 m

Simplifying the expression, we get:

Relative precision = 0.000578

To express the relative precision as a ratio, we invert the value and multiply it by a large number to get a whole number. In this case, we multiply by 1000:

Relative precision ratio = 1 / (0.000578) * 1000

Simplifying the expression further, we have:

Relative precision ratio = 1730

Therefore, the relative precision of this traverse is 1 : 1730, which corresponds to option B.

Explanation:

The relative precision ratio is a measure of the accuracy of the traverse. A smaller value indicates a higher accuracy, while a larger value indicates a lower accuracy. In this case, the relative precision ratio is 1730, which means that the accuracy of the traverse is relatively high.

It is important to note that the closing error is the difference between the measured and calculated values for the traverse. In this case, the closing error is 0.289 m, which indicates that there is a small discrepancy between the observed measurements and the mathematical model of the traverse.

Overall, the relative precision provides a quantitative measure of the accuracy of the traverse and helps assess the reliability of the surveying measurements.