1 sina = \frac{4}{5}; siny = \frac{3}{5}. a = 12. Найдите с.

По теореме синусов:

$$ \frac{a}{sin \alpha} = \frac{c}{sin \gamma} $$, где a = 12, $$sin \alpha = \frac{4}{5}, sin \gamma = \frac{3}{5}$$. Тогда:

$$ \frac{12}{\frac{4}{5}} = \frac{c}{\frac{3}{5}} $$ $$12 \cdot \frac{5}{4} = c \cdot \frac{5}{3}$$ $$15 = c \cdot \frac{5}{3}$$ $$c = \frac{15}{\frac{5}{3}}$$ $$c = 15 \cdot \frac{3}{5} = 9$$

Ответ: 9