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Question Number 177980 by infinityaction last updated on 11/Oct/22

Answered by mr W last updated on 11/Oct/22

Commented by mr W last updated on 11/Oct/22

$$\frac{EB}{\sin 144°}=\frac{1}{\sin x}$$$$\frac{EA}{\sin 36°}=\frac{1}{\sin 42°}$$$$\frac{EB}{\sin 84°}=\frac{EA}{\sin (30°-x)}$$$$\frac{\sin 144°}{\sin x\sin 84°}=\frac{\sin 36°}{\sin 42°\sin (30°-x)}$$$$\frac{\sin (30°-x)}{\sin x}=\frac{\sin 84°}{\sin 42°}=2\cos 42°$$$$\frac{1}{2\tan x}-\frac{\sqrt{3}}{2}=2\cos 42°$$$$\tan x=\frac{1}{4\cos 42°+\sqrt{3}}$$$$\Rightarrow x=12°$$

Commented by Tawa11 last updated on 11/Oct/22

$$\mathrm{Great}\mathrm{sir}$$

Commented by infinityaction last updated on 12/Oct/22

$$thankssir$$

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