For a closed traverse, the sum of latitudes is 4 m and the sum of departures is 3 m. The closing error for the traverse would be:
- A3 m
- B7 m
- C5 mCorrect
- D4 m
Solution
Concept
Closing error of a closed traverse is the resultant of the error in latitudes and the error in departures.
Formula
e = √((ΣL)2 + (ΣD)2)
Step-by-step solution
1. Sum of latitudes ΣL = 4 m 2. Sum of departures ΣD = 3 m 3. e = √(42 + 32) = √(16 + 9) = √25 4. e = 5 m
Explanation
In a perfect closed traverse, the sums of latitudes and departures are both zero. If they are not zero, the traverse does not close. The gap is the hypotenuse of a right triangle with sides ΣL and ΣD.
Why the other options are wrong
A (3 m) is only the departure error. B (7 m) is the simple sum 4 + 3, which is wrong because the two errors are at right angles. D (4 m) is only the latitude error.
Shortcut
3-4-5 triangle, so the answer is 5 m.
Common mistake
Adding ΣL and ΣD directly instead of using the Pythagoras rule.
Correct answer: C) 5 m