This is a right triangle with the lengths of one leg ($CB$) and the hypotenuse ($AB$) provided. The task is to calculate the length of the other leg ($AC$) using the Pythagorean Theorem:

$AB^2 = AC^2 + CB^2$

Step-by-step solution:

1. Substitute the known values:
   • $AB = 7 \, \text{cm}$
   • $CB = 4.5 \, \text{cm}$

$7^2 = AC^2 + 4.5^2$

2. Square the given lengths: $49 = AC^2 + 20.25$

3. Solve for $AC^2$: $AC^2 = 49 - 20.25 = 28.75$

4. Take the square root of both sides to find $AC$: $AC = \sqrt{28.75} \approx 5.36 \, \text{cm}$

Final Answer:

$AC \approx 5.36 \, \text{cm}$

Would you like further clarification or additional details?

Related Questions:

1. How does the Pythagorean Theorem apply to non-right triangles?
2. Can you explain why the square root is taken in the final step?
3. What are the conditions for using the Pythagorean Theorem?
4. How would the problem change if a different leg length was given?
5. How is this theorem used in real-world applications?

Tip:

Always check that the triangle is a right triangle before applying the Pythagorean Theorem!