1. The problem is to find the length of the hypotenuse or a missing side 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 always the side opposite the right angle (the longest side). 4. To find the hypotenuse $c$, rearrange the formula: $$c = \sqrt{a^2 + b^2}$$ 5. To find a missing leg (say $a$), rearrange: $$a = \sqrt{c^2 - b^2}$$ 6. Example: If $a=3$ and $b=4$, then $$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$ 7. This means the hypotenuse is 5 units long. This method applies to any right triangle to find the missing side length.