1. The problem is to understand when to add or subtract in the Pythagorean theorem context. 2. The Pythagorean theorem states that in a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relationship is: $$c^2 = a^2 + b^2$$ 3. This formula is used when you know the two legs and want to find the hypotenuse (the longest side). 4. If you know the hypotenuse and one leg, and want to find the other leg, you rearrange the formula: $$a^2 = c^2 - b^2$$ or $$b^2 = c^2 - a^2$$ 5. So, you add the squares of the legs to find the hypotenuse, and subtract the square of the known leg from the square of the hypotenuse to find the missing leg. 6. Important rule: The hypotenuse is always the longest side, so $c$ is always greater than $a$ and $b$. 7. Example: If $a=3$ and $b=4$, then $$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ $$c = \sqrt{25} = 5$$ 8. If $c=5$ and $a=3$, then $$b^2 = 5^2 - 3^2 = 25 - 9 = 16$$ $$b = \sqrt{16} = 4$$ This explains when to add or subtract in the Pythagorean theorem.