Question Number 71517 by TawaTawa last updated on 16/Oct/19
Answered by mind is power last updated on 16/Oct/19
$$\mathrm{AD}=\mathrm{x} \\ $$$$\frac{\mathrm{x}}{\mathrm{sin}\left(\theta\right)}=\frac{\mathrm{DC}}{\mathrm{sin}\left(\theta\right)}\Rightarrow\mathrm{1}=\frac{\mathrm{x}}{\mathrm{DC}} \\ $$$$\frac{\mathrm{x}}{\mathrm{sin}\left(\mathrm{3}\theta\right)}=\frac{\mathrm{DC}}{\mathrm{sin}\left(\mathrm{10}\theta\right)}\Rightarrow\frac{\mathrm{x}}{\mathrm{DC}}=\frac{\mathrm{sin}\left(\mathrm{3}\theta\right)}{\mathrm{sin}\left(\mathrm{10}\theta\right)} \\ $$$$ \\ $$$$\Rightarrow\mathrm{sin}\left(\mathrm{3}\theta\right)=\mathrm{sin}\left(\mathrm{10}\theta\right) \\ $$$$\mathrm{10}\theta\leqslant\mathrm{180} \\ $$$$\mathrm{sin}\left(\mathrm{3}\theta\right)=\mathrm{sin}\left(\mathrm{10}\theta\right)\Rightarrow\mathrm{10}\theta=\mathrm{180}−\mathrm{3}\theta \\ $$$$\Rightarrow\mathrm{13}\theta=\mathrm{180}\Rightarrow\theta=\frac{\mathrm{180}}{\mathrm{13}} \\ $$
Commented by TawaTawa last updated on 16/Oct/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$