Question Number 203704 by mnjuly1970 last updated on 26/Jan/24
$$ \\ $$$$\:\:\:\:\:{Q}:\:{In}\:{A}\overset{\Delta} {{B}C}\::\:\:\left(\:{AB}={AC}={b}\:\right)\:{and}\:\:\left(\:{BC}={a}\:\right).\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{If}\:\:,\:\:{cos}\:\left({A}\:\right)=\:\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:,\:\:\:\:{then}\:{find}\:{the}\:{value}\:{of}\::\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\frac{{b}}{{a}}\:}\:=? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\: \\ $$
Answered by esmaeil last updated on 26/Jan/24
$${BC}^{\mathrm{2}} ={AB}^{\mathrm{2}} +{AC}^{\mathrm{2}} −\mathrm{2}{AB}×{ACcosA}\rightarrow \\ $$$${a}^{\mathrm{2}} ={b}^{\mathrm{2}} +{b}^{\mathrm{2}} −\mathrm{2}{b}^{\mathrm{2}} {cosA}\rightarrow \\ $$$$\mathrm{3}{a}^{\mathrm{2}} =\mathrm{2}{b}^{\mathrm{2}} \rightarrow\sqrt{\frac{{b}}{{a}}}=\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$