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Question Number 71517 by TawaTawa last updated on 16/Oct/19

Answered by mind is power last updated on 16/Oct/19

$$\mathrm{AD}=\mathrm{x}$$$$\frac{\mathrm{x}}{\sin \left(\theta \right)}=\frac{\mathrm{DC}}{\sin \left(\theta \right)}\Rightarrow 1=\frac{\mathrm{x}}{\mathrm{DC}}$$$$\frac{\mathrm{x}}{\sin \left(3\theta \right)}=\frac{\mathrm{DC}}{\sin \left(10\theta \right)}\Rightarrow \frac{\mathrm{x}}{\mathrm{DC}}=\frac{\sin \left(3\theta \right)}{\sin \left(10\theta \right)}$$$$$$$$\Rightarrow \sin \left(3\theta \right)=\sin \left(10\theta \right)$$$$10\theta ⩽180$$$$\sin \left(3\theta \right)=\sin \left(10\theta \right)\Rightarrow 10\theta =180-3\theta$$$$\Rightarrow 13\theta =180\Rightarrow \theta =\frac{180}{13}$$

Commented by TawaTawa last updated on 16/Oct/19

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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