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Find u (remember u is the hypotenuse).

A. 2 square root 2 
B. the square root of 2
C. 2
D. 4

In the given right triangle, \( u \) is the hypotenuse, \( v \) is one leg, and the other leg is \( \sqrt{2} \). The angle opposite the leg \( \sqrt{2} \) is \( 45^\circ \).

We know the properties of a \( 45^\circ-45^\circ-90^\circ \) triangle:
- The legs are equal in length.
- The hypotenuse is \( \sqrt{2} \) times the length of each leg.

Given:
- One leg (\( \sqrt{2} \))

To find the hypotenuse (\( u \)) of the triangle:
\[ u = \sqrt{2} \times \sqrt{2} \]
\[ u = \sqrt{2}^2 \]
\[ u = 2 \]

Thus, \( u = 2 \).

The correct answer is:
**C. 2**

Would you like more details or have any questions about this solution?

Here are 5 questions you might want to ask next:
1. How do I solve for \( v \) in this triangle?
2. Can you explain the properties of special right triangles in more detail?
3. How can I use trigonometric functions to find sides of a right triangle?
4. How would the solution change if the given leg was different?
5. What are the steps to solve for sides of any right triangle given one side and one angle?

**Tip:** In a \( 45^\circ-45^\circ-90^\circ \) triangle, both legs are equal in length, and the hypotenuse is always \( \sqrt{2} \) times the length of one leg.

Learn how to find the hypotenuse of a 45-45-90 triangle when one leg length is given as √2. This problem involves understanding the properties of 45-45-90 triangles, where the hypotenuse is √2 times the length of each leg. Suitable for high school students studying geometry.

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