5) C x 135° A B 2 2√2

5) По теореме косинусов:

$$x^2 = (2\sqrt{2})^2 + 2^2 - 2 \cdot 2\sqrt{2} \cdot 2 \cdot \cos 135°$$ $$\cos 135° = -\frac{\sqrt{2}}{2}$$ $$x^2 = 8 + 4 - 8\sqrt{2} \cdot (-\frac{\sqrt{2}}{2})$$ $$x^2 = 12 + 4 \cdot 2 = 12 + 8 = 20$$ $$x = \sqrt{20} = 2\sqrt{5}$$ Ответ: $$2\sqrt{5}$$