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Corrected Latitude

The initial latitude for $S76-{15}^{\text{'}}-41"$ E ${210\mathrm{.}58}^{\text{'}}$ is:

$-50\mathrm{.}0112$

The residual for the latitudes is $-0\mathrm{.}0148$

The sum of the distances around the traverse is ${769\mathrm{.}35}^{\text{'}}$

What is the corrected latitude?