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To solve this problem using Pythagoras' theorem, we know that the triangle is a right-angled triangle with sides of lengths \(4.8 \, \text{cm}\) and \(2 \, \text{cm}\). We are tasked with finding the hypotenuse \(c\).

Pythagoras' theorem states:
\[
c^2 = a^2 + b^2
\]
where:
- \(c\) is the hypotenuse (the side we want to find),
- \(a = 4.8 \, \text{cm}\) is one leg,
- \(b = 2 \, \text{cm}\) is the other leg.

Now, let's calculate the hypotenuse \(c\).

\[
c = \sqrt{(4.8^2 + 2^2)}
\]

\[
c = \sqrt{(23.04 + 4)} = \sqrt{27.04}
\]

\[
c \approx 5.2 \, \text{cm} \, (\text{rounded to 1 decimal place}).
\]

So, the length of the hypotenuse is approximately \(5.2 \, \text{cm}\).

Would you like more details or have any other questions? Here are five related questions for further practice:

1. What would the length of the hypotenuse be if the base was increased to 6 cm, while keeping the height the same?
2. How would you calculate the area of the right-angled triangle?
3. If the hypotenuse was known, how could you determine one of the other sides using Pythagoras' theorem?
4. How is Pythagoras' theorem applied in three-dimensional space?
5. What are the limitations of using Pythagoras' theorem in non-Euclidean geometry?

**Tip:** Always ensure that the triangle is right-angled before applying Pythagoras' theorem.

Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. The triangle has sides of lengths 4.8 cm and 2 cm.

Learn how to calculate the length of the hypotenuse in a right-angled triangle using Pythagoras' theorem. This problem involves a triangle with sides 4.8 cm and 2 cm, and the solution explains the use of the Pythagorean theorem to find the hypotenuse.

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