The image you provided shows a right triangle with sides labeled $x$, $y$, and $z$. The lengths of the triangle's sides appear to be $z = 20$, $y = 10$, and you're asked to solve for $x$, $y$, and $z$, with the instructions to leave your answers in simplified radical form (no decimals).

To proceed, I need to identify if there's enough information to use the Pythagorean theorem or any other relationships. Let's focus on solving for $x$ and checking if the problem involves trigonometry or other properties.

I’ll begin by considering the Pythagorean theorem for right triangles:

$x^2 + y^2 = z^2$

With $y = 10$ and $z = 20$, we can substitute these values into the equation:

$x^2 + 10^2 = 20^2$ $x^2 + 100 = 400$ $x^2 = 400 - 100 = 300$ $x = \sqrt{300} = \sqrt{100 \times 3} = 10\sqrt{3}$

So, the value of $x = 10\sqrt{3}$.

Now, $y$ and $z$ are already given as 10 and 20 respectively.

Would you like me to explore any further details or clarify any part of the process?