In computing state plane coordinates for a project area whose mean orthometric height is $100\mathrm{.}997m,$ an average scale factor of $0\mathrm{.}99994959$ was used. The average geoid height for the area is $-22\mathrm{.}663m.$ The given distances between points in this project area were computed from SPCS$83$ state plane coordinates. What horizontal length would have to be observed to lay off these lines on the ground? $($Use $6,371,000m$ for an average radius for the Earth.$)$