Adjust the angles of triangle ABC for the following angular values and weights:

$($a$)A=58{15}^{\text{'}}{30}^{\text{'}\text{'}},w{t}_1$;$B=72{20}^{\text{'}}{40}^{\text{'}\text{'}},$ wt $3$;$C=49{23}^{\text{'}}{50}^{\text{'}\text{'}},wt{2}_{?}(5$pts$)$

$($b$)A=90{15}^{\text{'}}{10}^{\text{'}\text{'}},wt{3}_{\text{;}}B=45{40}^{\text{'}}{50}^{\text{'}\text{'}},wt{4}_{\text{;}}C=44{04}^{\text{'}}{00}^{\text{'}\text{'}},$ wt $2(5$pts$)$

A line of levels was run from benchmarks $A$ to $B,B$ to $C,$ and $C$ to $D.$ The elevation differences

obtained between benchmarks, with their standard deviations, are listed below. What is the

difference in elevation from benchmark A to D and the standard deviation of that elevation

difference?

a$.$ BM A to $BMB=+45\mathrm{.}62+-0\mathrm{.}10ft$;$BM$ B to $BMC=-80\mathrm{.}25+-0\mathrm{.}14ft$;$BMC$ to BM D

$=-70\mathrm{.}15+-0\mathrm{.}09ft(10pts)$

b$.$ BM A to $BMB=-55\mathrm{.}700+-0\mathrm{.}012m$;$BMB$ to $BMC=+85\mathrm{.}456321+-0\mathrm{.}018m$;$BM$

C to $BMD=+60\mathrm{.}789+-0\mathrm{.}013m(10$pts$)$