Question

In a closed traverse with five sides, the error found from the fore bearing and back bearing of the last line is + 1°. The correction to the third line will be:
1. 0°24'
2. 0°36'
3. 0°48'
4. 0°12'

Answer 1

Correct Answer - Option 2 : 0°36'

Concept:

In general, the closing error(e) in the traverse survey is given as:

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

reΣL = Summation of Latitudes of all lines involved in traverse or also called error in Latitude

ΣD = Summation of Departure of all lines involved in traverse or also called error in Departure

However, in a closed traverse in which bearings are observed, the closing error in bearing may be determined by observing the bearing of the last line, and correction in the bearing of the last line is the closing error.

Calculation:

Given data

Number of sides of closed traverse(n) = 5

Error(e) = 1^o

Now the correction on sides(or lines) of closed traverse as follows:

Correction to the first line

= e / n = 0°12′

Correction to the second line

= 2e /n = 0°24′

Correction to the third line

= 3e / n = 0°36′

Correction to the fourth line

= 4e / n =0°48′

Correction to the fifth line

= 5e / n = 1°0′