To find \( x \) in the triangle, let's assume that \( x \) refers to the same value as \( m \) (the hypotenuse), based on the typical labeling in right triangles where \( x \) or \( m \) is used to represent the hypotenuse. 

Given:
- Height = \( 7.5 \, \text{cm} \)
- Base = \( 15 \, \text{cm} \)
- Hypotenuse = \( x \, \text{cm} \) (assuming \( x = m \))

We use the Pythagorean theorem:

\[
x^2 = (\text{base})^2 + (\text{height})^2
\]

Substitute the given values:

\[
x^2 = (15 \, \text{cm})^2 + (7.5 \, \text{cm})^2
\]
\[
x^2 = 225 \, \text{cm}^2 + 56.25 \, \text{cm}^2
\]
\[
x^2 = 281.25 \, \text{cm}^2
\]

Taking the square root of both sides:

\[
x = \sqrt{281.25 \, \text{cm}^2}
\]
\[
x \approx 16.77 \, \text{cm}
\]

Thus, \( x \) is approximately \( 16.77 \, \text{cm} \).

Would you like further details or explanations?

Here are five related questions:
1. How can you verify the accuracy of the Pythagorean theorem in this context?
2. What happens if the triangle's sides are in different units? How would you handle the conversion?
3. What are the sine, cosine, and tangent of the angles in this triangle?
4. How does the calculation change if the triangle is not a right triangle?
5. Can you express the sides of the triangle as a ratio? What would that represent?

**Tip:** When dealing with squares and square roots, make sure to simplify your work as much as possible to avoid errors.

Discover how to find x in a right triangle using the Pythagorean theorem with a step-by-step solution. Given the base and height, calculate the hypotenuse using the Pythagorean theorem. Suitable for Grades 7-9 mathematics education.

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