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Question Number 176336 by mnjuly1970 last updated on 16/Sep/22

   in AB_  ^Δ C :  ((b−c)/(h_a  )) =k ,            and  A^�  is given.          B^�  , C^�  =?

$$ \\ $$$$\:{in}\:{A}\overset{\Delta} {{B}}_{\:} {C}\::\:\:\frac{{b}−{c}}{{h}_{{a}} \:}\:={k}\:, \\ $$$$\:\:\:\:\:\:\:\:\:\:{and}\:\:\hat {{A}}\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:\:\hat {{B}}\:,\:\hat {{C}}\:=?\:\: \\ $$

Answered by mr W last updated on 16/Sep/22

C=180°−A−B  c=(h_a /(sin B))  b=(h_a /(sin C))  ((b−c)/h_a )=(1/(sin C))−(1/(sin B))=k  ⇒(1/(sin (A+B)))−(1/(sin B))=k  we can solve for B only numerically.

$${C}=\mathrm{180}°−{A}−{B} \\ $$$${c}=\frac{{h}_{{a}} }{\mathrm{sin}\:{B}} \\ $$$${b}=\frac{{h}_{{a}} }{\mathrm{sin}\:{C}} \\ $$$$\frac{{b}−{c}}{{h}_{{a}} }=\frac{\mathrm{1}}{\mathrm{sin}\:{C}}−\frac{\mathrm{1}}{\mathrm{sin}\:{B}}={k} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{sin}\:\left({A}+{B}\right)}−\frac{\mathrm{1}}{\mathrm{sin}\:{B}}={k} \\ $$$${we}\:{can}\:{solve}\:{for}\:{B}\:{only}\:{numerically}. \\ $$

Answered by behi834171 last updated on 16/Sep/22

something else,is needed.  something,like:R...

$${something}\:{else},{is}\:{needed}. \\ $$$${something},{like}:\boldsymbol{{R}}... \\ $$

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