Problem $4$: A baseline for a pre$-$engineering survey runs down a steep hill. Rather than measure horizontally downhill with the steel tape, the vertical angle was measured with a theodolite and the slope distance with an EDM. The vertical angle was $30\backslash$deg $22\text{'},$ turned to a prism pole $4\mathrm{.}00$ft above the ground. The slope distance from the theodolite to the prism was $82\mathrm{.}18$ft$.$ The theodolite's optical center was $4\mathrm{.}72$ft above the upper baseline station at $2+72\mathrm{.}32.($a$)$ If the elevation of the upper station is $361\mathrm{.}29$ft$,$ what is the elevation of the lower station?$($b$)$ What is the chainage of the lower station?