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.