Question Number 164507 by mathlove last updated on 18/Jan/22
Commented by mathlove last updated on 18/Jan/22
$$\mathrm{tan}\theta=\frac{\mathrm{1}}{\mathrm{3}}\:\:{and}\:\:\:\mathrm{tan}\:\beta=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${faind}\:\:{a}\:\:{and}\:\:\:{b} \\ $$
Commented by mr W last updated on 18/Jan/22
$${not}\:{possible}!\:{question}\:{is}\:{wrong}! \\ $$$$\mathrm{tan}\:\beta=\frac{{a}}{{b}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${you}\:{can}\:{not}\:{determine}\:{a}\:{and}\:{b}. \\ $$
Answered by alephzero last updated on 18/Jan/22
$$\mathrm{tan}\:\theta\:=\:\frac{{AC}}{{BC}}\:=\:\frac{{a}}{{BC}}\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{tan}\:\beta\:=\:\frac{{AC}}{{CD}}\:=\:\frac{{a}}{{b}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{{a}}{{b}}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\Rightarrow\:{a}\:=\:\frac{\mathrm{3}{b}}{\mathrm{4}}\:\wedge\:{b}\:=\:\frac{\mathrm{4}{a}}{\mathrm{3}} \\ $$