The image shows two right-angled triangles. Find the values of x and y. Simplify all radicals.

Consider the upper right-angled triangle.
The vertical leg is $6 \text{ m}$.
The horizontal leg is $5 \text{ m}$.
The hypotenuse is $x \text{ m}$.
Applying the Pythagorean theorem:

$$x^2 = 6^2 + 5^2$$ $$x^2 = 36 + 25$$ $$x^2 = 61$$ $$x = \sqrt{61} \text{ m}$$

Consider the lower right-angled triangle.
The vertical leg is $y \text{ m}$.
The horizontal leg is $8 \text{ m}$.
The hypotenuse is $12 \text{ m}$.
Applying the Pythagorean theorem:

$$y^2 + 8^2 = 12^2$$ $$y^2 + 64 = 144$$

Subtract 64 from both sides:

$$y^2 = 144 - 64$$ $$y^2 = 80$$ $$y = \sqrt{80} \text{ m}$$

Simplify the square root:

$$y = \sqrt{16 \times 5}$$ $$y = 4\sqrt{5} \text{ m}$$

The values are:
$x = \boxed{\sqrt{61} \text{ m}}$
$y = \boxed{4\sqrt{5} \text{ m}}$