Find the elevation of a point at the end of an open traverse, when provided the elevation of a point at the beginning of the traverse, and the intermediate foresight and back sight measurements.

find the elevation at point F in feet in this problem points A through F are positioned along and open traverse survey data is provided which includes the back sight readings the for site readings and the elevation at Point a all length values in the data table are in units of feet the problem asks to find the elevation at point F in this analysis we'll begin with point a because we were given its elevation value from here we can relate the elevation between two consecutive points a and B using the back sight and foresight measurements the column labeled H I represents the height of the instrument or more precisely the elevation of the line-of-sight based on a vertical datum or benchmark before we can find the elevation at point F

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we first have to find the elevation at point B and then we'll work our way down to point F one point at a time if we take a closer look at points a and B we can better understand the leveling procedure from the problem statement we know the elevation at Point a equals eight hundred sixty two point zero nine feet if we place the measuring rod at point a and take a level reading from the instrument to the rod the back sight distance for point a is the vertical length from the ground up to the sited location on the rod as mentioned before the height of the instrument a B is the vertical distance between the datum and the elevation of the line of sight now we can compute the height of instrument a B as the elevation at point A plus the back sight reading at Point a which equals 867 point to four feet next the rod man sets the rod vertically at point B and the instrument man takes another level shot at the rod this reading on the rod represents the foresight elevation which in this case is four point B and for this example equals two point six four feet and the elevation at point B equals the vertical distance from the datum to point B which equals the height of the instrument - the foresight reading after plugging in the known values the elevation at point B equals eight hundred sixty four point six zero feet looking over our equations the elevation at point B equals the height of the instrument minus the foresight reading but previously we already solved for the height of the instrument as the elevation at point A plus the back sight reading to point a substituting in the height of the instrument we can equate the elevation of point B to the elevation at point A plus the back sight to point a minus the foresight to point B we can use this equation to find the elevation at point c by knowing the elevation at point B and the back sight to point B and the foresight to Point C the elevation at Point C equals eight hundred sixty seven point zero nine feet we'll continue to use this equation to solve for the elevation at Point D E and F the elevation at Point D equals the elevation at Point C plus the backside of Point C minus the four side Point D which equals eight hundred seventy three point zero nine feet the elevation for point E is calculated the same way and equals eight hundred seventy eight point six nine feet and finally the elevation at point F equals eight hundred seventy four point three eight feet when reviewing the possible solutions the answer is C

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