Inverse Pythagorean theorem
Ok, so have you ever heard of something called the Pythagorean theorem? No? Well, it's a fancy math rule that tells us how to find the length of a diagonal line (also known as a hypotenuse) when we have two sides of a right triangle.
But what's a right triangle, you might ask? Great question! It's a triangle that has one angle that measures exactly 90 degrees, like a square.
So, let's say we have a right triangle with two sides that measure 3 and 4 units. We can use the Pythagorean theorem to find the length of the hypotenuse by adding the squares of the two shorter sides together and then taking the square root of that sum.
So, in our example, we would do 3 squared (which is 9) plus 4 squared (which is 16), which equals 25. Then, we take the square root of 25, which is 5. So, the length of the hypotenuse in our triangle is 5 units.
Now, what about the inverse Pythagorean theorem? Well, "inverse" just means the opposite of something. So, if the Pythagorean theorem tells us how to find the hypotenuse when we know the other sides, then the inverse Pythagorean theorem tells us how to find one of the other sides when we know the hypotenuse and the other side.
Let's use our same triangle example. We know that the hypotenuse is 5 units and one of the shorter sides is 3 units. We can use the inverse Pythagorean theorem to find the length of the other shorter side by subtracting the square of the known side from the square of the hypotenuse, and then taking the square root of that difference.
So, we would do 5 squared (which is 25) minus 3 squared (which is 9), which equals 16. Then, we take the square root of 16, which is 4. So, the length of the other side in our triangle is 4 units.
Ta-da! That's the inverse Pythagorean theorem in action - using fancy math rules to find the missing pieces of a right triangle puzzle.
But what's a right triangle, you might ask? Great question! It's a triangle that has one angle that measures exactly 90 degrees, like a square.
So, let's say we have a right triangle with two sides that measure 3 and 4 units. We can use the Pythagorean theorem to find the length of the hypotenuse by adding the squares of the two shorter sides together and then taking the square root of that sum.
So, in our example, we would do 3 squared (which is 9) plus 4 squared (which is 16), which equals 25. Then, we take the square root of 25, which is 5. So, the length of the hypotenuse in our triangle is 5 units.
Now, what about the inverse Pythagorean theorem? Well, "inverse" just means the opposite of something. So, if the Pythagorean theorem tells us how to find the hypotenuse when we know the other sides, then the inverse Pythagorean theorem tells us how to find one of the other sides when we know the hypotenuse and the other side.
Let's use our same triangle example. We know that the hypotenuse is 5 units and one of the shorter sides is 3 units. We can use the inverse Pythagorean theorem to find the length of the other shorter side by subtracting the square of the known side from the square of the hypotenuse, and then taking the square root of that difference.
So, we would do 5 squared (which is 25) minus 3 squared (which is 9), which equals 16. Then, we take the square root of 16, which is 4. So, the length of the other side in our triangle is 4 units.
Ta-da! That's the inverse Pythagorean theorem in action - using fancy math rules to find the missing pieces of a right triangle puzzle.