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To find \( u \) in the given right triangle with a \( 45^\circ \) angle and hypotenuse \( \sqrt{2} \), we can use the properties of a \( 45^\circ-45^\circ-90^\circ \) triangle.

In a \( 45^\circ-45^\circ-90^\circ \) triangle, the legs are equal, and each leg is \( \frac{\text{hypotenuse}}{\sqrt{2}} \).

Given:
- Hypotenuse (\( \sqrt{2} \))
- One of the angles (\( 45^\circ \))

We need to find \( u \) (the base of the triangle).

For a \( 45^\circ-45^\circ-90^\circ \) triangle:
\[ u = \frac{\sqrt{2}}{\sqrt{2}} = 1 \]

Thus, \( u = 1 \).

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 the same triangle?
2. Can you explain the properties of a \( 45^\circ-45^\circ-90^\circ \) triangle in more detail?
3. How would the solution change if the hypotenuse was a different length?
4. What are the general steps to solve for the sides of a right triangle given one angle and one side?
5. How can I apply trigonometric functions to find the sides of a right triangle?

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

Learn how to find the base u in a 45°-45°-90° triangle where the hypotenuse is √2. Detailed step-by-step solution using the properties of a 45°-45°-90° triangle. Suitable for high school students.

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