Verified answer

Ответ:

AC = 2 см

Объяснение:

По теореме синусов

[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) } [/tex]

B = 30°

AB = 2√2 см

C = 45°

[tex] \frac{2 \sqrt{2} }{ \sin(45) } = \frac{ac}{ \sin(30) } \\ \frac{2 \sqrt{2} }{ \frac{ \sqrt{2} }{2} } = \frac{ac}{ \frac{1}{2} } \\ \\ ac = \frac{ 2 \sqrt{2} \times \frac{1}{2} }{ \frac{ \sqrt{2} }{2} } = \frac{ \sqrt{2} }{ \frac{ \sqrt{2} }{2} } = = \sqrt{2} \times \frac{2}{ \sqrt{2} } = 2[/tex]