Question Number 176336 by mnjuly1970 last updated on 16/Sep/22
$$ \\ $$$$\:{in}\:{A}\overset{\Delta} {{B}}_{\:} {C}\::\:\:\frac{{b}−{c}}{{h}_{{a}} \:}\:={k}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:{and}\:\:\hat {{A}}\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\:\hat {{B}}\:,\:\hat {{C}}\:=?\:\: \\ $$
Answered by mr W last updated on 16/Sep/22
$${C}=\mathrm{180}°−{A}−{B} \\ $$$${c}=\frac{{h}_{{a}} }{\mathrm{sin}\:{B}} \\ $$$${b}=\frac{{h}_{{a}} }{\mathrm{sin}\:{C}} \\ $$$$\frac{{b}−{c}}{{h}_{{a}} }=\frac{\mathrm{1}}{\mathrm{sin}\:{C}}−\frac{\mathrm{1}}{\mathrm{sin}\:{B}}={k} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{sin}\:\left({A}+{B}\right)}−\frac{\mathrm{1}}{\mathrm{sin}\:{B}}={k} \\ $$$${we}\:{can}\:{solve}\:{for}\:{B}\:{only}\:{numerically}. \\ $$
Answered by behi834171 last updated on 16/Sep/22
$${something}\:{else},{is}\:{needed}. \\ $$$${something},{like}:\boldsymbol{{R}}… \\ $$