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To solve the problem of finding the height \( X \) in the triangle, we'll analyze the given information. The triangle appears to be a right triangle, where one side is labeled as the height \( X \), the base is labeled with a known distance (which seems to be 6 meters from the image), and the hypotenuse is also provided (indicated as 10 meters).

### Step-by-Step Solution:

1. **Identify the Right Triangle:** 
   Since the triangle is a right triangle, we can apply the Pythagorean theorem, which states:
   \[
   \text{(Hypotenuse)}^2 = \text{(Base)}^2 + \text{(Height)}^2
   \]

2. **Apply the Pythagorean Theorem:**
   Given:
   - Hypotenuse \( = 10 \, \text{meters} \)
   - Base \( = 6 \, \text{meters} \)
   - Height \( = X \, \text{meters} \)

   The Pythagorean theorem will be:
   \[
   10^2 = 6^2 + X^2
   \]

   Simplifying this:
   \[
   100 = 36 + X^2
   \]

3. **Solve for \( X \):**
   \[
   X^2 = 100 - 36
   \]
   \[
   X^2 = 64
   \]
   \[
   X = \sqrt{64}
   \]
   \[
   X = 8 \, \text{meters}
   \]

So, the height \( X \) in the triangle is \( 8 \) meters.

Would you like more details or have any questions?

### Relative Questions:
1. How does the Pythagorean theorem apply to different types of triangles?
2. What are the other trigonometric relationships in a right triangle?
3. How can you find the length of the hypotenuse if only the height and base are known?
4. What is the significance of understanding triangle properties in geometry?
5. How does the Pythagorean theorem extend to three-dimensional shapes?

**Tip:** Always double-check the measurements and the type of triangle before applying the Pythagorean theorem to ensure accurate results.

Learn how to find the height X in a triangle using the Pythagorean theorem with a detailed step-by-step solution. This problem covers key geometric concepts, including the Pythagorean theorem for right triangles. Suitable for students in Grades 7-9.

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