Let's solve the problem using the Pythagorean theorem.

The triangle in the image is a right triangle, where:

• Hypotenuse $c = 15$,
• One leg $a = 9$,
• The other leg $b = x$ (which we need to find).

The Pythagorean theorem states: $a^2 + b^2 = c^2$ Substitute the known values: $9^2 + x^2 = 15^2$ $81 + x^2 = 225$ Now, isolate $x^2$: $x^2 = 225 - 81 = 144$ Take the square root of both sides: $x = \sqrt{144} = 12$

So, the correct answer is: $\boxed{C} \quad x = 12$

Let me know if you have any questions or need further clarification!

Here are 5 follow-up questions to explore the topic further:

1. How does the Pythagorean theorem apply to 3D shapes like pyramids or cubes?
2. Can the Pythagorean theorem be used for non-right triangles?
3. How do you determine which side is the hypotenuse in any right triangle?
4. What happens if one of the triangle’s sides is given as a square root value?
5. Can the Pythagorean theorem help in real-world problems, such as navigation?

Tip: Always verify which side is the hypotenuse in a right triangle—it’s the longest side and always opposite the right angle.