1. Problem: Find the length of the hypotenuse in a right triangle using the Pythagorean theorem. 2. The Pythagorean 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. Important rules: - The triangle must be right-angled. - $c$ is the side opposite the right angle (the longest side). 4. Example: If $a=3$ and $b=4$, then: $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ 5. Taking the square root of both sides: $$c = \sqrt{25} = 5$$ 6. So, the hypotenuse length is 5. This theorem helps find the missing side in right triangles easily.