Question Number 209458 by SonGoku last updated on 10/Jul/24
Commented by SonGoku last updated on 10/Jul/24
$$\mathrm{l}\:=\:?\: \\ $$$$\mathrm{BC}\:=\:\:\mathrm{l}\:+\:\mathrm{200m} \\ $$$$\mathrm{B}\hat {\mathrm{A}C}\:=\:\mathrm{120}° \\ $$$$\mathrm{A}\hat {\mathrm{B}C}\:=\:\mathrm{38}°\mathrm{12}'\mathrm{48}'' \\ $$
Commented by mr W last updated on 10/Jul/24
$$\frac{{BC}}{\mathrm{sin}\:\angle{BAC}}=\frac{{AC}}{\mathrm{sin}\:\angle{ABC}} \\ $$$$\frac{{l}+\mathrm{200}}{\mathrm{sin}\:\mathrm{120}°}=\frac{{l}}{\mathrm{sin}\:\mathrm{38}°\mathrm{12}'\mathrm{48}''} \\ $$$${l}=\frac{\mathrm{200}}{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}\:\mathrm{sin}\:\mathrm{38}°\mathrm{12}'\mathrm{48}''}−\mathrm{1}}=\mathrm{500}\:{m} \\ $$
Commented by SonGoku last updated on 10/Jul/24
$$\mathrm{Thank}\:\mathrm{you} \\ $$