Problem 1 (Top Triangle):

$$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\sin(30^\circ) = \frac{x}{8}$$ $$x = 8 \times \sin(30^\circ)$$ $$x = 8 \times \frac{1}{2}$$ $$x = 4$$

$$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ $$\cos(30^\circ) = \frac{y}{8}$$ $$y = 8 \times \cos(30^\circ)$$ $$y = 8 \times \frac{\sqrt{3}}{2}$$ $$y = 4\sqrt{3}$$

The values are: $\boxed{x = 4, y = 4\sqrt{3}}$

** (Bottom Triangle):**
We have a right-angled triangle with a hypotenuse of 2 and an angle of $45^\circ$. We need to find the adjacent side $x$ and the opposite side $y$.

$$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ $$\cos(45^\circ) = \frac{x}{2}$$ $$x = 2 \times \cos(45^\circ)$$ $$x = 2 \times \frac{\sqrt{2}}{2}$$ $$x = \sqrt{2}$$

$$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ $$\sin(45^\circ) = \frac{y}{2}$$ $$y = 2 \times \sin(45^\circ)$$ $$y = 2 \times \frac{\sqrt{2}}{2}$$ $$y = \sqrt{2}$$

The values are: $\boxed{x = \sqrt{2}, y = \sqrt{2}}$