The triangle in the image provided is a right triangle with side lengths of 12 and 9. To find the missing hypotenuse (denoted as $c$), we can use the Pythagorean theorem:

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

Here, $a = 12$ and $b = 9$.

Let's calculate the value of $c$.The hypotenuse of the right triangle is $15$.

Would you like further details or explanations? Here are some related questions to deepen your understanding:

1. How does the Pythagorean theorem apply to different types of triangles?
2. What are some real-world applications of the Pythagorean theorem?
3. How can you use trigonometry (e.g., sine, cosine) to find angles in this triangle?
4. Can you find the area of the triangle with the given sides?
5. What other methods could be used to solve for the hypotenuse?

Tip: Always check if a triangle is a right triangle before applying the Pythagorean theorem.