Final answer:
The Pythagorean Theorem is used to calculate the length of the hypotenuse of a right triangle by summing the squares of the other two sides and taking the square root. The formula is a² + b² = c², which simplifies to c = √a² + b² to find the hypotenuse.
Step-by-step explanation:
Using the Pythagorean Theorem
In mathematics, the Pythagorean Theorem is a fundamental principle that describes the relation between the lengths of the sides of a right triangle. Specifically, it states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship can be expressed as a² + b² = c². To find the length of the hypotenuse, you can rearrange this formula to c = √a² + b².
When given the lengths of the two legs of the triangle, you can compute the length of the hypotenuse by substituting the values into the formula. For example, if the lengths are 9 units and 5 units, the length of the hypotenuse would be calculated as √(9 units)² + (5 units)². After computing the squares and summing them, you take the square root to find the length of the hypotenuse, which in this case is √(81 + 25) = √106 = 10.3 units (rounded to one decimal place).