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!