A line is recorded as $572\mathrm{.}90m$ long. It is measured with a $0\mathrm{.}65kg$ tape which is $30\mathrm{.}005m$ long at $20C$ under a $50N$ pull supported at both ends. During measurement, the temperature is $5C$ and the tape is suspended under a $75N$ pull. The line is measured on $3\%$ grade, $E=200$GPa, the cross$-$sectional area of tape is $3m{m}^2$ and the coefficient of linear expansion is $0\mathrm{.}0000116\frac{m}{}C.$

a$.$ Compute the actual length of tape during measurement.

b$.$ Compute the total error to be corrected for the inclined distance. $($ANSWER THIS$)$

What is the true horizontal distance?