Pythagorean Theorem: Finding the Length of the Hypotenuse | Math with Mr. J

Introduction to the Pythagorean Theorem00:00:00

The video introduces the Pythagorean theorem, a² + b² = c², where 'c' always represents the hypotenuse and 'a' and 'b' represent the legs of a right triangle. This theorem is used to find the length of a missing side when two sides are known.

Example 1: Finding Hypotenuse with Whole Numbers00:00:36

The first example demonstrates finding the hypotenuse with legs of 8 meters and 6 meters. By substituting these values into the formula (8² + 6² = c²), the equation becomes 64 + 36 = c², leading to 100 = c². Taking the square root of both sides, 'c' is found to be 10 meters.

Example 2: Finding Hypotenuse with a Non-Perfect Square Result00:03:11

The second example involves legs of 10 feet and 7 feet. Plugging these into the theorem (10² + 7² = c²) results in 100 + 49 = c², or 149 = c². Since 149 is not a perfect square, the hypotenuse 'c' is approximately 12.21 feet when rounded to the hundredths place. The process of taking the square root and rounding the irrational number is explained.

Conclusion00:06:23

The video concludes by reiterating the steps to find the hypotenuse using the Pythagorean theorem, summarizing the methods demonstrated for both whole number and approximate decimal solutions.