Question Number 28139 by math solver last updated on 21/Jan/18
Answered by mrW2 last updated on 21/Jan/18
$${A}=\frac{\pi}{\mathrm{2}}−{B} \\ $$$$\frac{{A}−{B}}{\mathrm{2}}=\frac{\pi}{\mathrm{4}}−{B} \\ $$$$\mathrm{tan}\:\left(\frac{{A}−{B}}{\mathrm{2}}\right)=\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{B}\right)=\frac{\mathrm{1}−\mathrm{tan}\:{B}}{\mathrm{1}+\mathrm{tan}\:{B}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{4}−\mathrm{4}\:\mathrm{tan}\:{B}=\mathrm{1}+\mathrm{tan}\:{B} \\ $$$$\Rightarrow\mathrm{tan}\:{B}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\frac{{x}}{{y}}=\frac{{b}}{{a}}=\mathrm{tan}\:{B}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\Rightarrow{Answer}\:\left({D}\right) \\ $$
Commented by math solver last updated on 21/Jan/18
$${thank}\:{you}\:{sir}\:! \\ $$