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Question Number 206659 by cherokeesay last updated on 21/Apr/24

Answered by mr W last updated on 21/Apr/24

Commented by mr W last updated on 21/Apr/24

$$\tan \alpha =\frac{1}{2}$$$$a=2R\sin \alpha =\frac{2R}{\sqrt{5}}$$$$\beta =\frac{\pi }{4}-\alpha$$$$\tan \beta =\frac{1-\tan \alpha }{1+\tan \alpha }=\frac{1-\frac{1}{2}}{1+\frac{1}{2}}=\frac{1}{3}$$$$b=2R\sin \beta =\frac{2R}{\sqrt{10}}$$$$\Rightarrow \frac{a}{b}=\frac{\sqrt{10}}{\sqrt{5}}=\sqrt{2}$$

Commented by cherokeesay last updated on 21/Apr/24

$$nice!thankyou!$$

Commented by MM42 last updated on 23/Apr/24

$$\underset{―}{\underbrace{⋚}}$$

Answered by MM42 last updated on 23/Apr/24

$$sin\alpha =\frac{1}{\sqrt{5}}\mathrm{\&}cos\alpha =\frac{2}{\sqrt{5}}\mathrm{\&}\theta =\alpha +\beta =45$$$$\frac{b}{sin(90+\alpha )}=\frac{1}{sin\theta }\Rightarrow b=\frac{4}{\sqrt{10}}$$$$a=4sin\alpha =\frac{4}{\sqrt{5}}$$$$\Rightarrow \frac{a}{b}=\sqrt{2}✓$$

Commented by MM42 last updated on 23/Apr/24

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