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Question-71517




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

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