To calculate the hypotenuse of this right-angled triangle using Pythagoras' theorem, we follow these steps:

Pythagoras' Theorem:

$c^2 = a^2 + b^2$ Where:

• $c$ is the hypotenuse,
• $a$ and $b$ are the two shorter sides.

Here:

• $a = 3 \, \text{cm}$
• $b = 1.6 \, \text{cm}$

Step-by-Step Calculation:

1. Square each side: $a^2 = 3^2 = 9$ $b^2 = 1.6^2 = 2.56$

2. Add the squares: $c^2 = a^2 + b^2 = 9 + 2.56 = 11.56$

3. Take the square root to find $c$ (the hypotenuse): $c = \sqrt{11.56} \approx 3.4$

Final Answer:

The length of the hypotenuse is 3.4 cm (to 1 decimal place).

Would you like a more detailed explanation or further clarification?

Related Questions:

1. How do you rearrange Pythagoras' theorem to find a shorter side?
2. What are real-life applications of Pythagoras' theorem?
3. Can Pythagoras' theorem be used for non-right-angled triangles?
4. How can I calculate the area of this triangle?
5. What happens if I scale both sides of a triangle proportionally?

Tip:

Always check if the triangle is right-angled before applying Pythagoras' theorem.