$4-2.$ An angle ABC in Fig. $4-3$ is determined by linear measurements in the manner described in Section $4-2.$ If $BD=BE=100ft$ and $k=47\mathrm{.}76ft,$ what is the value of the angle $($nearest minute$)?$

$4-3.$ A signal has been displaced $0\mathrm{.}18ft$ perpendicular to the line of sight of a theodolite. If the signal is $850ft$ away from the instrument, what angular error is introduced $($nearest second$)?$

$4-4.$ A line rod is $\frac{1}{2}$ in$.$ in diameter. What angle would be subtended between the two sides at a distance of $180ft($nearest second$)?$

$4-5.$ In Problem $4-4,$ if the instrument is $240m$ away, what angle would the line rod subtend $($nearest second$)?$