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Question Number 186079 by TUN last updated on 31/Jan/23

Answered by a.lgnaoui last updated on 01/Feb/23

$$△ABDet△ACDAD:cotecommun$$$$△ABD:$$$$\frac{\sin 46}{\mathrm{BD}}=\frac{\sin \mathrm{X}}{\mathrm{AD}}\left(1\right)$$$$△ACD$$$$\frac{\sin 12}{\mathrm{CD}}=\frac{\sin 62}{\mathrm{AD}}\left(2\right)$$$$\left(1\right)\mathrm{et}\left(2\right)\Rightarrow \frac{\mathrm{BDsin}\mathrm{X}}{\sin 46}=\frac{\mathrm{CDsin}62}{\sin 12}\left(3\right)$$$$△BCD\measuredangle CDB=52-\mathrm{X}$$$$\frac{\sin 8}{\mathrm{BD}}=\frac{\sin (52-\mathrm{X})}{\mathrm{CD}}\left(4\right)$$$$\left(3\right)\times \left(4\right)\Rightarrow \frac{\sin 8\times \sin \mathrm{X}}{\sin 46}=\frac{\sin 62\times \sin (52-\mathrm{X})}{\sin 12}$$$$\sin 8\times \sin 12\times \sin \mathrm{X}=\sin 62\times \sin 46\sin (52-\mathrm{X})$$$$\sin (52-\mathrm{X})=\sin 52\sqrt{1-{\sin }^2\mathrm{X}}-\cos 52\sin \mathrm{X}$$$$posins\mathrm{Z}=\sin \mathrm{X}$$$$\frac{\sin \mathrm{X}}{\sin (52-\mathrm{X})}=\frac{\sin 62\times \sin 46}{\sin 8\times \sin 12}$$$$$$$$=\frac{\sin \mathrm{X}}{\sin 52\cos \mathrm{X}-\cos 52\sin \mathrm{X}}=\frac{\sin 62\times \sin 46}{\sin 8\times \sin 12}$$$$=\frac{\left(\tan \mathrm{X}\right)}{(\sin 52-\cos 52\tan \mathrm{X})}=\frac{\sin 62\times \sin 46}{\sin 8\times \sin 12}$$$$posinst=\tan \mathrm{X}$$$$\frac{t}{\sin 52-t\cos 52}=\frac{\sin 62\times \sin 46}{\sin 8\times \sin 12}$$$$t(\sin 8\sin 12+\sin 62\sin 46\cos 52)=\sin 52\sin 62\sin 46)$$$$t=\frac{\sin 52\sin 62\sin 46}{\sin 8\sin 12+\sin 62\sin 46\cos 52}$$$$t=1,191753592594$$$$$$$$\mathbf{X}=50°$$

Commented by a.lgnaoui last updated on 01/Feb/23

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