Let's analyze the image provided and solve for $y$ in figure (II).

The image contains three right triangles. To solve for $y$, we can use the Pythagorean theorem, which states:

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

Where:

• $a$ and $b$ are the two legs of the right triangle.
• $c$ is the hypotenuse (the longest side).

Step-by-step solution for Figure (II):

• One leg $a = 15$
• Another leg $b = 9$
• Hypotenuse $y$ is unknown.

By the Pythagorean theorem:

$15^2 + 9^2 = y^2$

$225 + 81 = y^2$

$306 = y^2$

Taking the square root of both sides:

$y = \sqrt{306} \approx 17.49$

Thus, $y \approx 17.49$.

Would you like further clarification or additional details?

Related Questions:

1. What would happen if the Pythagorean theorem is applied incorrectly?
2. How is the Pythagorean theorem used in other fields, like physics?
3. What are other ways to find the length of a side in a right triangle besides the Pythagorean theorem?
4. Could there be a scenario where the triangle is not a right triangle in the given question?
5. Can you solve triangles with angles instead of side lengths?

Tip: The Pythagorean theorem only works for right-angled triangles!