Problem $2(10$ points$)$

You setup a total station on point A with a height of instrument of $5\mathrm{.}32ft.$ You sight a prism on location $B$ and measure a slope distance of $230\mathrm{.}6$ ft and a vertical angle of $82{41}^{\text{'}}{36}^{\text{'}\text{'}}.$ The height of target was set to an elevation of $6\mathrm{.}12$ ft $.$ The measured horizontal angle $($an azimuth was determined to be $43{21}^{\text{'}}{42}^{\text{'}\text{'}}.$

$($a$)$ Determine the elevation of location B if the elevation of $A$ is $430\mathrm{.}16$ feet.

$($b$)$ Point A is known to have a northing of $5000$ ft and an easting of $4325$ ft $.$ Determine the northing and easting of point $B$ and express as a coordinate of the form $($E$,$ N$,$ Z$).$