Pythagoras Theorem Ef5E4C

1. **State the problem:** The Pythagorean theorem helps us find the length of a side in a right triangle. 2. **Formula:** The theorem states that in a right triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two sides ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. **Explanation:** Here, $c$ is the side opposite the right angle (the longest side), and $a$ and $b$ are the other two sides. 4. **How to use it:** - If you know $a$ and $b$, find $c$ by calculating $$c = \sqrt{a^2 + b^2}$$. - If you know $c$ and one side, say $a$, find the other side $b$ by rearranging: $$b^2 = c^2 - a^2$$ and then $$b = \sqrt{c^2 - a^2}$$ 5. **Example:** Suppose $a=3$ and $b=4$, then $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ So, $$c = \sqrt{25} = 5$$ This means the hypotenuse is 5 units long. 6. **Summary:** Use the formula $$c^2 = a^2 + b^2$$ to find the missing side of a right triangle by squaring the known sides, adding or subtracting as needed, and then taking the square root.