Question

The following table gives data of consecutive coordinate in respect of a closed theodolite traverse PQRSP.

Station	Northing (m)	Southing (m)	Easting (m)	Westing (m)
P	400.75			300.5
Q	100.25		199.25
R		199.0	299.75
S		300.0		200.5

The magnitude and direction of error of closure in whole circle bearing are

• A. $2.0\text{m and}{45}^{\circ }$
• B. $3.42\text{m and}{45}^{\circ }$
• C. $2.0\text{m and}{315}^{\circ }$
• D. $2.82\text{m and}{315}^{\circ }$

Answer 1

The correct option is D $2.82\text{m and}{315}^{\circ }$

Error in Latitude,

$\Delta L=\sum L$

$=400.75+100.25-199-300=2$

Error in departure,

$\Delta D=\sum D$

$=199.5+299.75-300.5-200.5$

$=-2$

Closing error,

$=\sqrt{(2{)}^2+(-2{)}^2}=2\sqrt{2}=2.82m$

Since $\Delta L$ is positive and $\Delta D$ is negative, the line of closure is in $4^{th}$ quadrant.

$\theta ={\tan }^{-1}\left(\frac{-2}{2}\right)=-{45}^{\circ }$

W.C.B of closing error,

$=360-45={315}^{\circ }$