So, I have a question on a project that asks why you get a different answer when measuring the side of a hypotenuse versus using the Pythagorean Theorem. I did get different answers, but I just can't figure out why.
It would be great if you could answer this please!!
I'm just bumping this up to the top of the page.
The only reason I can think of is that a measurement is subject to error (and is really only a decimal approximation), whereas the PT results is exact.
Hey thanks Steve!
Great question! Let's break it down step by step.
First, let's define the Pythagorean Theorem. It states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Now, when you measure the length of the hypotenuse directly with a ruler or any other measuring tool, you are obtaining the actual length of the side. This measurement gives you a real value.
However, when you use the Pythagorean Theorem to find the length of the hypotenuse, you are calculating it based on the lengths of the other two sides. This involves squaring the lengths of the other sides, summing them, and then taking the square root of that sum. This calculation might involve rounding or approximation at different steps.
Due to the nature of rounding or approximation, especially if you are working with decimal values or using calculators with limited precision, you might end up with a slightly different result when using the Pythagorean Theorem compared to the actual measured length.
So, the difference arises due to the inherent limitations of calculations involving rounding or approximation, rather than an error in the Pythagorean Theorem itself.
To summarize, when measuring the length of the hypotenuse directly, you obtain the actual length. But when using the Pythagorean Theorem, calculations involving rounding or approximation may lead to a slightly different result.