https://file.aiquickdraw.com/mathbot/file/1727195482017vncqfy0a.jpg

This image shows a right triangle, with a perpendicular height of 7 cm, a slant height (hypotenuse) of 9 cm, and the base labeled as \(x\) cm. Additionally, there is an angle \(\theta\) on the right side of the triangle.

To solve for \(x\), we can use the Pythagorean theorem, which states:

\[
c^2 = a^2 + b^2
\]

Where:
- \(c\) is the hypotenuse (9 cm),
- \(a\) is the height (7 cm),
- \(b\) is the base (\(x\)).

Let's calculate \(x\) using this formula.

\[
9^2 = 7^2 + x^2
\]

\[
81 = 49 + x^2
\]

\[
x^2 = 81 - 49
\]

\[
x^2 = 32
\]

\[
x = \sqrt{32} \approx 5.66 \, \text{cm}
\]

So, \(x \approx 5.66 \, \text{cm}\).

Would you like further details or have any questions? 

Here are 5 related questions:
1. How can we calculate the area of this triangle?
2. What is the value of \(\theta\) using trigonometry?
3. How do we find the perimeter of this triangle?
4. What other methods can be used to solve for \(x\)?
5. What is the significance of the right angle in the triangle's properties?

**Tip:** In any right triangle, the Pythagorean theorem is a powerful tool for solving for unknown sides when two sides are given.

What is the value of x in a right triangle with a height of 7 cm, a hypotenuse of 9 cm, and an unknown base x?

Learn how to find the base (x) of a right triangle with a height of 7 cm and a hypotenuse of 9 cm using the Pythagorean Theorem. This problem demonstrates step-by-step application of the theorem and covers key concepts in right triangle geometry.

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