Pythagorean Theorem Explained with Animations

Now that we understand the basic formula, let's see a visual proof of how it works.On our 3-4-5 right triangle, we'll create squares on each side.The square on side 'a' has an area of nine square units.The square on side 'b' has an area of sixteen square units.And the square on the hypotenuse has an area of twenty-five square units.Let's see how these areas are made up of unit squares.When we add the nine square units from a squared, plus the sixteen square units from b squared...We get exactly twenty-five square units, which is the area of the square on the hypotenuse!This visual proof shows us that the areas of the squares on the two shorter sides combine to equal the area of the square on the hypotenuse.Let's see how the Pythagorean theorem helps solve real-world problems, starting with a ladder against a wall.If we have a 15-foot ladder and need it to reach 12 feet up the wall, we can calculate how far to place it from the wall.Using the Pythagorean theorem, we can verify these measurements are correct.TV manufacturers use the Pythagorean theorem to calculate screen sizes, which are measured diagonally.For a TV that's 48 inches wide and 27 inches tall, we can calculate the diagonal measurement.Let's verify this common 55-inch TV size using our theorem.Construction workers and architects use the Pythagorean theorem to verify right angles and measure diagonal distances.For a rectangular foundation that's 40 feet wide and 20 feet long, we can calculate the diagonal measurement to ensure square corners.Let's calculate the diagonal distance to verify our foundation is square.