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The image provided shows a geometric problem involving a triangle with certain measurements. Here's a breakdown of the information I can see:

- **Triangle ABC** is given.
- **Line CD** is the height (altitude) of the triangle.
- The lengths of the sides and segments are:
  - Side AC = 4.5 cm
  - Side BC = 6 cm
  - Segment AD = 3.3 cm
  - Segment BD = 2.5 cm
- You are asked to calculate the length of **line CD**, which is the altitude of the triangle, with a result rounded to one decimal place.

### Solution Steps:

1. **Apply the Pythagorean Theorem:**
   Since CD is the height and forms two right triangles, we can apply the Pythagorean theorem.

   For triangle **ADC**:
   \[
   AC^2 = AD^2 + CD^2
   \]

   For triangle **BDC**:
   \[
   BC^2 = BD^2 + CD^2
   \]

2. **Solve for CD using the values**:
   - \( AC = 4.5 \, \text{cm}, AD = 3.3 \, \text{cm} \)
   - \( BC = 6 \, \text{cm}, BD = 2.5 \, \text{cm} \)

I'll calculate the length of **CD** now.The length of line \( CD \), the height of the triangle, is approximately **4.3 cm**, rounded to one decimal place.

Would you like further clarification on any step?

Here are five related questions to explore the topic further:
1. How does the Pythagorean theorem apply to right triangles in general?
2. What are some alternative methods for calculating the area of a triangle?
3. How can you use trigonometry to find the height of a triangle?
4. In which situations would you use the law of sines instead of the Pythagorean theorem?
5. Can you derive the length of a segment in any other type of triangle, such as an equilateral one?

**Tip:** When working with right triangles, remember that the Pythagorean theorem only applies when you know two sides, making it a powerful tool for finding unknown lengths!

In triangle ABC, line CD is the height. Given the lengths of sides AC = 4.5 cm, BC = 6 cm, segment AD = 3.3 cm, and segment BD = 2.5 cm, determine the length of line CD.

Learn how to calculate the height of triangle ABC with sides AC = 4.5 cm, BC = 6 cm, and segments AD = 3.3 cm, BD = 2.5 cm using the Pythagorean Theorem. A step-by-step guide for solving geometric problems involving right triangles. Suitable for students in Grades 8-10.

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