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Question Number 164507 by mathlove last updated on 18/Jan/22

Commented by mathlove last updated on 18/Jan/22

$$\tan \theta =\frac{1}{3}and\tan \beta =\frac{3}{4}$$$$faindaandb$$

Commented by mr W last updated on 18/Jan/22

$$notpossible!questioniswrong!$$$$\tan \beta =\frac{a}{b}=\frac{3}{4}$$$$youcannotdetermineaandb.$$

Answered by alephzero last updated on 18/Jan/22

$$\tan \theta =\frac{AC}{BC}=\frac{a}{BC}=\frac{1}{3}$$$$\tan \beta =\frac{AC}{CD}=\frac{a}{b}=\frac{3}{4}$$$$\frac{a}{b}=\frac{3}{4}\Rightarrow a=\frac{3b}{4}\wedge b=\frac{4a}{3}$$

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