MHB Finding Angle C in Triangle ABC

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In triangle ABC, with angle B measuring 30 degrees, the relationship between the sides is given by the equation BC² - AB² = AB × AC. To find angle C, one can apply the Law of Cosines or manipulate the given equation. The problem requires solving for angle C based on the established conditions. The solution involves using trigonometric identities or geometric properties to derive the angle. Ultimately, the goal is to determine the measure of angle C accurately.
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$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$
 
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Albert said:
$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\
find \,\, \angle C=?$
hint
prove $\angle A=2\angle C$
 
Albert said:
$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}---(1)\\
find \,\, \angle C=?$
more hint:
in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet
 
Albert said:
more hint:
in fact $\angle B=30^o$ is not important, you should prove for any triangle if $\angle A=2\angle C $ then (1) will meet
my solution :
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