In a 45-degree right triangle, the properties of the triangle are such that the lengths of the two legs are equal, and the relationship between the length of a leg \( a \) and the hypotenuse \( c \) can be given by the formula:
\[ c = a \sqrt{2} \]
Let's first analyze the second triangle which has a side opposite the 45-degree angle of length \( 4\sqrt{2} \). Since this is a 45-degree right triangle, the lengths of both legs are equal, meaning the other leg is also \( 4\sqrt{2} \).
Now, we can find the length of the hypotenuse \( c \):
\[ c = a \sqrt{2} \] Substituting \( a = 4\sqrt{2} \):
\[ c = (4\sqrt{2}) \sqrt{2} \] \[ c = 4 \cdot 2 \] \[ c = 8 \]
Now we can conclude that the hypotenuse of the second triangle has a length of \( 8 \).
Thus, the correct answer is:
B. The hypotenuse of the second triangle has length 8.
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