The Pythagoras Theorem    

The Pythagoras theorem is the mathematical formula used to find the hypotenuse of a right-angle triangle. In other words, it is used to find the longest side of a 90-degree triangle. The formula is the following: a squared plus b squared equals c squared. This sentence does not make that much sense on its own, but with proper context it works. “a” and “b” refer to the legs (the legs are the two sides of the triangle that are not the hypotenuse) and the “c” refers to the hypotenuse. 

To further explain the concept; this equation is done by first squaring the lengths of the two legs individually. Once the legs have been squared, they are added together. If you take that result and find its square root, that will be the length of the hypotenuse. 

To get a better understanding, here’s a couple examples: 

First, let’s say that a = 3 and b = 4. If a (3) x a (3) = 9, and b (4) x b (4) = 16, we can add them together to get 25. 25 can then be reduced to its square root of 5, and there is your c value, the length of the hypotenuse. 

For a more complicated example, we will say that a = 8 and b = 11. 8 x 8 = 64 and 11 x 11 = 121. We add those together to get 185. Now, this example is not just more difficult because it has bigger numbers, we also must estimate. While we could use a calculator, in this unit we learned to estimate square roots, so we should use that skill. If we know that 185 lies between 169 (13²) and 196. (14²) We can now estimate by placing our “guess” between those two numbers. 185 lies slightly closer to 196, so we can say it is about 13.6 or 13.7. This means that c ≈13.6.