$6\mathrm{.}6$ For the following data, compute the horizontal distance for a recorded slope dis$-$ tance AB$,($a$)$ AB $356\mathrm{.}96$ ft$,$ slope angle $=5\backslash$deg $07($b$)$ AB $243\mathrm{.}876$ m$,$ difference in elevation A to B $10\mathrm{.}350$ m A $100$ ft steel tape of cross$-$sectional area $0\mathrm{.}0025$ in$\mathrm{.}2,$ weight $2\mathrm{.}0$ lb$,$ and standard$-$ ized at $68\backslash$deg F is $99\mathrm{.}983$ ft between end marks when supported throughout under a $10-$lb pull. What is the true horizontal length of a recorded distance AB for the conditions given in Problems $6\mathrm{.}7$ through $6\mathrm{.}12?($Assume horizontal taping and all full tape lengths except the last.$)$