We can use the Pythagorean theorem to solve for the missing side $x$ in this right triangle. The Pythagorean theorem is given as:

$a^2 + b^2 = c^2$

Where $a$ and $b$ are the legs of the right triangle, and $c$ is the hypotenuse. In this triangle, the hypotenuse is the side labeled $x$, and the legs are 11 cm and 16 cm.

So, we will calculate $x$ by solving:

$x^2 = 11^2 + 16^2$

$x^2 = 121 + 256$

$x^2 = 377$

Now, take the square root of both sides to find $x$:

$x = \sqrt{377} \approx 19.4 \, \text{cm}$

Thus, the length of the missing side $x$ is approximately 19.4 cm.

Would you like a further breakdown or have any questions?

Here are 5 related questions for deeper understanding:

1. How can the Pythagorean theorem be used in different types of right triangles?
2. Can the Pythagorean theorem be applied in non-right triangles? Why or why not?
3. What is the significance of the hypotenuse in a right triangle?
4. How do we estimate square roots when solving for a missing side in the Pythagorean theorem?
5. In what real-life scenarios can you apply the Pythagorean theorem?

Tip: Always double-check your calculations when solving square roots to avoid small errors that may affect accuracy.