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Question Number 182078 by Acem last updated on 04/Dec/22

Answered by mr W last updated on 05/Dec/22

$$\frac{\sin 30}{\sin (30-\theta )}=\frac{\sin (30+\theta )}{\sin \theta }$$$$\frac{\sin \theta }{2}=\frac{(\cos \theta +\sqrt{3}\sin \theta )(\cos \theta -\sqrt{3}\sin \theta )}{4}$$$$2\sin \theta ={\cos }^2\theta -3{\sin }^2\theta$$$$4{\sin }^2\theta +2\sin \theta -1=0$$$$\sin \theta =\frac{-1+\sqrt{5}}{4}\Rightarrow \theta =18°$$

Commented by manxsol last updated on 04/Dec/22

Commented by manxsol last updated on 04/Dec/22

$$thans,SirW$$

Commented by mr W last updated on 05/Dec/22

$$thanksforaddingtheexplanation!$$

Commented by manxsol last updated on 05/Dec/22

$$SometimesI{don}^{\prime }tunderstand$$$$apartofyourexplanation.$$$${That}^{\prime }swhy{I}^{\prime }mlooking$$$$forhow?hedidit.$$$$YouanSirAcemareagreatguide$$

Commented by Acem last updated on 05/Dec/22

$$VerywellSirW,thankyouforyoursharing!$$$$P.s,justfix\sin \theta =\frac{\sqrt{5}-1}{4}Thankyou$$$$$$

Commented by Acem last updated on 05/Dec/22

$$@Mr.Manxsol,Thankyouwithallmyheart!$$$$Andthankyouagainforsharing:)$$$$$$$$Well,{It}^{\prime }sagoodnewsthatyoutodayhavesolved$$$$ourfriendMr.W{}^{\prime }scode(:Goahead!$$$$$$$$Bytheway,{what}^{\prime }sabouttheblackboardyou$$$$writeon?ilikedit,isitrealoraplasmascreen?$$$$$$$$Mybro,youcancheckoutthesolutionwith$$$$othermethodbelow,butkeepyouruseofthelaws$$$$causesometimeswemayfailatthe$$$$Euclidianmethod,but{it}^{\prime }smoreinteresting!$$$$$$$$Hope{you}^{\prime }realwaysdoingwell!$$$$$$

Answered by Acem last updated on 05/Dec/22

$$EuclideanSolution$$

Commented by Acem last updated on 05/Dec/22

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