Question: explain Pythagoras theorem
1. **Problem Statement:**
The Pythagoras theorem states a fundamental relation in a right-angled triangle between the lengths of the sides.
2. **Theorem Formula:**
For a right triangle with legs of lengths $a$ and $b$, and hypotenuse length $c$, the theorem states:
$$c^2 = a^2 + b^2$$
3. **Explanation:**
This means the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
4. **Important Rules:**
- The triangle must be right-angled.
- $c$ is always the longest side.
5. **Example:**
If $a = 3$ and $b = 4$, then:
$$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$
Taking the square root:
$$c = \sqrt{25} = 5$$
6. **Interpretation:**
This theorem helps find the length of one side if the other two are known, and is widely used in geometry, trigonometry, and real-world applications.