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Question Number 124953 by Algoritm last updated on 07/Dec/20

Answered by mr W last updated on 07/Dec/20

$$sayAC=1$$$$\frac{BC}{\sin 30}=\frac{AC}{\sin 50}$$$$\Rightarrow BC=\frac{\sin 30}{\sin 50}$$$$similarly$$$$OC=\frac{\sin 10}{\sin 20}$$$$\frac{\sin (\alpha +10)}{\sin \alpha }=\frac{BC}{OC}=\frac{\sin 30\times \sin 20}{\sin 50\times \sin 10}$$$$\cos 10+\frac{\sin 10}{\tan \alpha }=\frac{\sin 30\times \sin 20}{\sin 50\times \sin 10}$$$$\tan \alpha =\frac{\sin 10}{\frac{\sin 30\times \sin 20}{\sin 50\times \sin 10}-\cos 10}=\frac{1}{\sqrt{3}}$$$$\Rightarrow \alpha =30°$$

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