Odpowiedź:
Szczegółowe wyjaśnienie:
Wykorzystajmy tw. sinusów
[tex]\frac{a}{sin\alpha} = \frac{b}{sin\beta} = \frac{c}{sin\gamma} = 2R[/tex]
[tex]\frac{a}{sin\alpha} = 2R[/tex]
[tex]sin\alpha = \frac{a}{2R} = \frac{10}{20} = \frac{1}{2}[/tex]
[tex]sin^2\alpha + cos^2\alpha = 1\\cos\alpha = \sqrt{1 - sin^2\alpha}[/tex]
[tex]cos\alpha = \sqrt{1-(\frac{1}{2})^2} = \frac{\sqrt3}{2}[/tex]
[tex]\frac{b}{sin\beta} = 2R[/tex]
[tex]sin\beta = \frac{14}{20} = \frac{7}{10}[/tex]
[tex]cos\beta = \sqrt{1 - (\frac{7}{10})^2} = \frac{\sqrt{51}}{10}[/tex]
[tex]\gamma = 180^o - (\alpha + \beta)[/tex]
[tex]\frac{c}{sin\gamma} = 2R\\c = 2R\sin\gamma = 20 * sin(180 - (\alpha+\beta)) = 20 * sin(\alpha+\beta) =\\20*[sin\alpha*cos\beta + cos\alpha*sin\beta] = 20 *[\frac{1}{2}*\frac{\sqrt{51}}{10} + \frac{\sqrt{3}}{2}*\frac{7}{10} = 20*\frac{\sqrt{51}+7\sqrt{3}}{20} = \sqrt{51}+7\sqrt{3}[/tex]
