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Question Number 163292 by amin96 last updated on 05/Jan/22

Answered by mr W last updated on 05/Jan/22

$$sayCD=AD=1$$$$AC=2\cos 10°$$$$\frac{BC}{\sin 20}=\frac{AC}{\sin (30+20)}$$$$\Rightarrow BC=\frac{2\cos 10\sin 20}{\sin 50}$$$$\frac{\sin x}{BC}=\frac{\sin (180-x-20)}{CD}$$$$\frac{\sin 50}{2\cos 10\sin 20}=\frac{\sin (x+20)}{\sin x}$$$$\frac{\sin 50}{2\cos 10\sin 20}=\cos 20+\frac{\sin 20}{\tan x}$$$$\tan x=\frac{\sin 20}{\frac{\sin 50}{2\cos 10\sin 20}-\cos 20}=\sqrt{3}$$$$\Rightarrow x=60°$$

Commented by Tawa11 last updated on 06/Jan/22

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

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