All problem$-$solving need to include the identify the techniques, i$.$e$.$ the formula$($s$)$ that you use to

solve the problem.

$9\mathrm{.}13$ An elevation must be established on a benchmark on an island that is

$520\mathrm{.}02ft$ from the nearest benchmark on the lake's shore. The surveyor

decides to use a total station that has a stated distance measuring

accuracy of $+-(3mm+3ppm)$ and a vertical compensator accurate to

within $+-{0\mathrm{.}4}^{\text{'}\text{'}}.$ The height of the instrument was $5\mathrm{.}26ft$ with an estimated

error of $+-0\mathrm{.}1ft.$ The prism height was $6\mathrm{.}00ft$ with an estimated error

of $+-0\mathrm{.}01ft.$ The single zenith angle is read as $96{07}^{\text{'}}{34}^{\text{'}\text{'}}.$ The estimated

errors in instrument and target centering are $+-0\mathrm{.}003ft.$ If the elevation

of the occupied benchmark is $85\mathrm{.}57ft,$ what is the corrected benchmark

elevation on the island? $($Assume that the instrument does not correct

for Earth curvature and refraction.$)$