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Question Number 74697 by chess1 last updated on 29/Nov/19

Answered by mr W last updated on 29/Nov/19

$$letBC=1$$$$DC=\frac{\sin 6}{\sin 24}$$$$AC=\frac{\sin 24}{\sin 54}$$$$\frac{\sin (12+x)}{\sin x}=\frac{\sin 24\times \sin 24}{\sin 54\times \sin 6}$$$$\frac{\sin 12}{\tan x}+\cos 12=\frac{\sin 24\times \sin 24}{\sin 54\times \sin 6}$$$$\tan x=\frac{\sin 12}{\frac{\sin 24\times \sin 24}{\sin 54\times \sin 6}-\cos 12}$$$$\Rightarrow x={\tan }^{-1}\left(\frac{\sin 12}{\frac{\sin 24\times \sin 24}{\sin 54\times \sin 6}-\cos 12}\right)=12°$$

Commented by chess1 last updated on 29/Nov/19

$$\mathrm{thanks}$$

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