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The problem you've provided is related to a 45°-45°-90° right triangle. In this type of triangle, the two legs are equal, and the hypotenuse is \( x \). The ratio between the legs and the hypotenuse is given by the following relationship:

\[
x = \text{{leg}} \times \sqrt{2}
\]

Here, one leg is given as 8. Therefore:

\[
x = 8 \times \sqrt{2}
\]

So, \( x = 8\sqrt{2} \).

The correct answer is **C: \( 8\sqrt{2} \)**.

Would you like more details or further questions on this?

### Related Questions:
1. What is the general formula for finding the hypotenuse in a 45°-45°-90° triangle?
2. How can you derive the side ratios for special right triangles like 30°-60°-90° and 45°-45°-90°?
3. If one leg of a 45°-45°-90° triangle is doubled, how does the hypotenuse change?
4. How would you calculate the hypotenuse if the given leg was \( 16 \)?
5. What is the Pythagorean theorem, and how is it applied to general right triangles?

### Tip:
Always check if the triangle in question is a special right triangle (like 45°-45°-90° or 30°-60°-90°), as these have standard ratio relationships that make solving easier.

Find the value of x in a 45°-45°-90° triangle where one leg is 8.

Learn how to find the hypotenuse in a 45°-45°-90° triangle where one leg is 8. This step-by-step solution uses the formula x = leg * sqrt(2) to calculate the hypotenuse. Ideal for students in Grades 8-10 studying geometry and special right triangles.

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