Which of the following is correct formula for closing error in traversing? (where, ∑L= algebraic sum of latitudes, ∑D = algebraic sum of departure, e = closing error)

Concept:

The equation for closing error and angle fo misclosure is given by,

\({\rm{e}} = \sqrt {{{\left( {{\rm{Σ L}}} \right)}^2} + {{\left( {{\rm{Σ D}}} \right)}^2}} \)

\({\rm{\theta }} = {\tan ^{ - 1}}\left[ {\frac{{{\rm{Σ D}}}}{{{\rm{Σ L}}}}} \right]\)

Where,

e = closing error, θ = angle of misclosure

ΣL = Algebraic sum of latitudes of all lines  

ΣD = Algebraic sum of departures of all lines

Important Points 

Latitude: It is the length (L) of projection of a line onto the North-South (L cosθ) axis.

Northing → Positive, Southing → Negative

Departure: It is the projection of the line (L) onto the east-west (L sinθ) axis.

Easting → Positive, Westing → Negative