Question

If the sum of northings of a traverse exceeds the sum of southings by 1 m and sum of eastings exceeds the sum of westings by 1m, the resultant closing error and its true bearing are respectively ;

• A. $2m,N{45}^{o}E$
• B. $2m,N{45}^{o}E$
• C. $1m,N{45}^{o}E$
• D. $\sqrt{2}m;N/{45}^{o}E$

Answer 1

The correct option is D $\sqrt{2}m;N/{45}^{o}E$

$\sum L=+1m$

$\sum D=+1m$

$Resultantclosingerror=\sqrt{(\sum L{)}^2+(\sum D{)}^2}$

$=\sqrt{(1{)}^2+(1{)}^2}=\sqrt{2}m$

$Truebearing,\theta =ta{n}^{-1}\left(\frac{\sum D}{\sum L}\right)=ta{n}^{-1}\left(\frac{1}{1}\right)={45}^o$

Since error lies in the first quadrant hence the bearing of error is $N{45}^{o}E$ .