Find the value of x in the right triangle where one side is 9 and there is a 45-degree angle.

Understand the Problem

The question is asking us to find the value of x in a right triangle with one angle of 45 degrees and a side length of 9. Since it's a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, and we can use this property to determine the value of x.

Answer

$x = 9$

Steps to Solve

Identify triangle properties

Since this is a 45-45-90 triangle, both legs are of equal length. The ratio of the sides in a 45-45-90 triangle is $1:1:\sqrt{2}$.

Set up the equation

Let both legs (the two sides opposite the 45-degree angles) be equal to $x$. Since one side is given as 9, we have:

$$ x = 9 $$

Conclusion of leg lengths

Thus, both legs of the triangle are equal, so we can conclude:

$$ x = 9 $$

The value of $x$ is $9$.

More Information

In a 45-45-90 triangle, the angles are always 45 degrees, making it isosceles. This means both legs have the same length, simplifying calculations significantly.

Tips

Assuming the angles affect side lengths: In 45-45-90 triangles, the angles ensure the legs are equal, which is crucial to remember.
Forgetting the properties of right triangles: Recognizing the specific ratio of sides in special triangles helps avoid confusion.

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