The image shows a right triangle with a vertical line dividing it into two smaller right triangles. The hypotenuse of the large triangle is labeled as $z$, and the other two sides of this large triangle are $11$ and $25$.

To solve for $z$, we can apply the Pythagorean theorem to the larger triangle, which relates the sides of a right triangle:

$z^2 = 11^2 + 25^2$

Now, let's calculate:

$z^2 = 121 + 625 = 746$

Taking the square root of both sides:

$z = \sqrt{746} \approx 27.3$

Thus, $z \approx 27.3$.

Would you like more details or explanations on this?

Here are 5 related questions you might want to explore:

1. How does the Pythagorean theorem apply to non-right triangles?
2. What is the importance of the altitude in this type of geometric problem?
3. How do we use trigonometric ratios to find angles in right triangles?
4. How can we find the area of a right triangle using different methods?
5. Can you apply the Pythagorean theorem to 3D problems?

Tip: When solving geometric problems, always check if smaller triangles within a larger one are similar, which can simplify calculations.