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Let's break down the problem.

We are dealing with two 45-45-90 right triangles, which have the following properties:
- The sides opposite the 45° angles are equal.
- The hypotenuse is \( \sqrt{2} \) times the length of each of the legs.

### Triangle 1:
- Hypotenuse = 16
- One of the legs = \( 8\sqrt{2} \)

To confirm the given leg of the triangle, we use the property of 45-45-90 triangles:  
\[
\text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}} = \frac{16}{\sqrt{2}} = 8\sqrt{2}
\]
This matches what was provided.

### Triangle 2:
- One of the legs = \( 4\sqrt{2} \)

To find the hypotenuse of this triangle, we apply the same rule for 45-45-90 triangles:
\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2} = 4\sqrt{2} \times \sqrt{2} = 4 \times 2 = 8
\]

So, the hypotenuse of the second triangle is 8, which matches the second answer choice.

### Answer:
The correct option is:
- "The hypotenuse of the second triangle has length 8."

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Would you like more details on any part of this solution? Here are some related questions for practice:

1. How do you calculate the hypotenuse in a 45-45-90 triangle given one leg?
2. What are the properties of 45-45-90 triangles?
3. Can you derive the hypotenuse if only the perimeter of a right triangle is given?
4. How do you find the legs of a 45-45-90 triangle given the hypotenuse?
5. What other types of right triangles have specific side ratio properties?

**Tip**: In a 45-45-90 triangle, both legs are always equal, and the hypotenuse is always \( \sqrt{2} \) times longer than either leg.

A right triangle has a hypotenuse of length 16 and an angle of 45°, with a side opposite this angle of length 8√2. A second right triangle also has an angle of 45° and a side opposite this angle with a length of 4√2. Determine the length of the hypotenuse in the second triangle.

Learn how to calculate the hypotenuse of a 45-45-90 triangle given the length of one leg. This problem demonstrates key geometric properties of right triangles with a detailed step-by-step solution. Suitable for students in Grades 9-11.

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