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В \(\triangle ABC\) известно, что \(\angle B=90\degree\) , \(AC=10\) , \(\angle C=30\degree\) . Найди \(AB\) и \(BC\) .

Решение.

\(\sin \angle C = \dfrac{AB}{AC} = \dfrac{AB}{10} = \sin 30\degree = \dfrac{1}{2} \Rightarrow AB=\) [ ].

\(\cos \angle C = \dfrac{BC}{AC} = \dfrac{BC}{10} = \cos 30\degree =\) [ \(\frac{1}{2}\) | \(\frac{\sqrt2}{2}\) | \(\frac{\sqrt3}{2}\) ] \(\Rightarrow BC=\) [ \(\frac{5}{\sqrt3}\) | \(\frac{\sqrt3}{20}\) | \(5\sqrt3\) | \(20\sqrt3\) ].

Ответ: \(AB=\) [ ], \(BC=\) [ \(\frac{5}{\sqrt3}\) | \(\frac{\sqrt3}{20}\) | \(5\sqrt3\) | \(20\sqrt3\) ].