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Question Number 124820 by enter last updated on 06/Dec/20

Answered by mr W last updated on 13/Jun/21

Commented by mr W last updated on 13/Jun/21

$$AC=2\cos 10°$$$$\frac{BC}{\sin 30°}=\frac{AC}{\sin 130°}$$$$BC=\frac{\cos 10°}{\sin 50°}$$$$\frac{\sin (\alpha +10)}{BC}=\frac{\sin \alpha }{OC}$$$$\cos 10°+\frac{\sin 10°}{\tan \alpha }=\frac{\cos 10°}{\sin 50°}$$$$\frac{\tan 10°}{\tan \alpha }=\frac{1}{\sin 50°}-1$$$$\Rightarrow \tan \alpha =\frac{\tan 10°}{\frac{1}{\sin 50°}-1}$$$$\Rightarrow \alpha =30°$$

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