The actual answer is x=34.9868 degrees approximately. How do we get that?
The first observation is that in a triangle ABC, where b=AC=2 and c=AB=1 and angle BAC=x, the cosine rule tells us that a^2=b^2+c^2-2bccosA=5-4cosx. Therefore a=sqrt(5-4cosx).
So 1=6tanx(1-1/a)=6tanx(a-1)/a and according to the sine rule: sinx/a=sinB/2=sinC; tanx=a/(6(a-1)).
and according to the cosine rule: cosA=cosx=(5-a^2)/4; cosB=(a^2-3)/2a; cosC=(a^2+3)/4a.
tanx=sinx/cosx=
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