Question

In a closed traverse, the sum of the latitudes is 1.39 m and the sum of the departures is 2.17 m. The Length and Whole Circle Bearing of the closing error are

• A. Length = 2.57 m, Whole Circle Bearing = 58°
• B. Length = 2.57 m, Whole Circle Bearing = 57°
• C. Length = 2.67 m, Whole Circle Bearing = 58°
• D. Length = 2.67 m, Whole Circle Bearing = 57°

Hint:

In surveying, the closing error is calculated using the sum of latitudes and the sum of departures. The Pythagorean theorem gives the error length, and the arctangent function helps calculate the bearing of the closing error.

Answer 1

The Correct Option is B

In surveying, the closing error in a traverse is the difference between the starting and ending points of the traverse. To calculate the closing error, we use the sum of the latitudes (north-south components) and the sum of the departures (east-west components). The closing error can be expressed in terms of its length and its direction (bearing).
Step 1: Calculate the Closing Error Length
The length of the closing error can be calculated using the Pythagorean theorem: \[ \text{Length of closing error} = \sqrt{(\text{Sum of latitudes})^2 + (\text{Sum of departures})^2} \] Given: \[ \text{Sum of latitudes} = 1.39 \, \text{m}, \quad \text{Sum of departures} = 2.17 \, \text{m} \] Substituting the values: \[ \text{Length of closing error} = \sqrt{(1.39)^2 + (2.17)^2} = \sqrt{1.9321 + 4.7089} = \sqrt{6.641} \approx 2.57 \, \text{m} \] Thus, the length of the closing error is approximately 2.57 m.
Step 2: Calculate the Whole Circle Bearing
The Whole Circle Bearing (WCB) of the closing error is the angle between the sum of the latitudes and the sum of the departures, which can be found using the formula: \[ \text{WCB} = \tan^{-1}\left(\frac{\text{Sum of latitudes}}{\text{Sum of departures}}\right) \] Substituting the given values: \[ \text{WCB} = \tan^{-1}\left(\frac{1.39}{2.17}\right) = \tan^{-1}(0.6406) \approx 57^\circ \] Thus, the Whole Circle Bearing of the closing error is approximately 57°.
Therefore, the correct answer is (B), Length = 2.57 m and Whole Circle Bearing = 57°.