Question

In measuring a round of angle at a station O, the third angle C closing the horizon is obtained from the relation C = 360° - (A + B). If angle A and B have the standard errors of $\pm 8^{\prime \prime }and\pm 6^{\prime \prime }$ respectively, the standard error of angle 'C' will be

• A. $\pm 7^{\prime \prime }$
• B. $\pm {10}^{\prime \prime }$
• C. $\pm {14}^{\prime \prime }$
• D. $\pm 2^{\prime \prime }$

Answer 1

The correct option is B $\pm {10}^{\prime \prime }$

$e_C^2={[\frac{\partial (360{}^{\circ }-A-B)}{\partial A}.e_A]}^2+[\frac{\partial (360{}^{\circ }-A-B)}{\partial B}.e_B]$

$\Rightarrow e_C^2=e_A^2+e_B^2$

$\Rightarrow e_C=\pm \sqrt{e_A^2+e_B^2}$

$=\pm \sqrt{{\left(8\right)}^2+{\left(6\right)}^2}$

$=\pm {10}^{\prime \prime }$