https://r2.erweima.ai/mathbot/image/1721871853230oddf68ew.png

To find \( u \) in the given right triangle with one angle of 45 degrees, we can use the properties of 45-45-90 triangles.

In a 45-45-90 triangle:
- The legs are equal.
- The hypotenuse is \(\sqrt{2}\) times the length of each leg.

Given:
- Hypotenuse \( = \sqrt{2} \)

Let's denote the legs as \( v \) and \( u \). Since this is a 45-45-90 triangle, we have:
\[
v = u
\]

And the relationship between the legs and the hypotenuse in a 45-45-90 triangle is:
\[
\text{Hypotenuse} = \sqrt{2} \times \text{leg}
\]

Substituting the known values:
\[
\sqrt{2} = \sqrt{2} \times u
\]

Solving for \( u \):
\[
u = 1
\]

Therefore, the value of \( u \) is \( 1 \).

Would you like more details or have any questions?

Here are 5 questions you might ask next:
1. How do you determine the sides of a 45-45-90 triangle?
2. Can you explain the properties of special right triangles?
3. What are the other types of special right triangles?
4. How do you use trigonometric ratios to solve for unknown sides?
5. Can you show an example of a 30-60-90 triangle problem?

**Tip:** When dealing with special right triangles like 45-45-90 or 30-60-90 triangles, remember their specific side ratios to quickly find missing lengths.

Discover how to find the value of u in a 45-45-90 triangle using its unique properties. This problem involves understanding the side ratios and relationships in special right triangles. Suitable for high school students learning geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation