Onyx_O14 :
The Pythagorean Theorem is a rule in geometry that applies only to right-angled triangles. In such a triangle, one angle is exactly 90 degrees, and the side opposite this right angle is called the hypotenuse, which is always the longest side. The two shorter sides are called the legs. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula is written as a² + b² = c², where a and b are the legs and c is the hypotenuse. To use the formula, first make sure you are working with a right-angled triangle. Then identify the sides: the two legs (a and b) and the hypotenuse (c). If you know the lengths of both legs, you can find the hypotenuse by squaring both legs, adding the results together, and then taking the square root of that sum. For example, if one leg is 3 units long and the other is 4 units long, you calculate 3² + 4² = 9 + 16 = 25, then take the square root of 25, which is 5. So the hypotenuse is 5 units long. You can also use the theorem to find a missing leg. If you know one leg and the hypotenuse, rearrange the formula to a² = c² - b², then solve for a. For example, if the hypotenuse is 13 and one leg is 5, then a² = 13² - 5² = 169 - 25 = 144, so a = √144 = 12. The Pythagorean Theorem is useful in many real-world situations, such as construction, navigation, and finding distances. It only works with right-angled triangles and is one of the most important tools in basic geometry.
2025-06-23 17:31:00