To find the length of the third side in this right triangle, we can apply the Pythagorean Theorem, which states that in a right triangle:

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

where $c$ is the hypotenuse and $a$ and $b$ are the other two sides.

Given:

• $a = 9$
• $b = 12$

Let's find $c$:

$c^2 = 9^2 + 12^2$ $c^2 = 81 + 144$ $c^2 = 225$ $c = \sqrt{225} = 15$

So, the length of the third side (hypotenuse) is $15$.

Would you like more details or have any questions about this?

Here are five related questions you might find interesting:

1. How can the Pythagorean Theorem be used in real-life applications?
2. What are some examples of right triangles in architecture or design?
3. How would you find the length of a side if given the hypotenuse and one leg?
4. How do you use trigonometric functions to find angles in a right triangle?
5. Can the Pythagorean Theorem be used in non-Euclidean geometry?

Tip: The Pythagorean Theorem only works for right triangles, so always check if you have a right angle first before applying it!