Pythagorean Theorem
That Pythagoras. I’m sure many students would like to flick his ear for coming up with his Pythagorean Theorem. I wonder how many thousands, or millions, of hours of homework have been focused on finding the hypotenuse of a right triangle? How many kids have spent their time coming through a story problem to figure out that the three lengths given in the problem were parts of a right triangle, then working backwards to find the height of a building, or a tree?Well, it’s not as hard as some may think. The Pythagorean Theorem is pretty simple. You can almost think of it as a recipe. You have certain ingredients that you need, some instructions on how to put together those ingredients, and the final outcome. So let’s try and look at it that way.
Pythagorean Theorem Formula
Ingredients: A right triangle – This is a triangle that has one 90 degree angle and 3 sides. (But, honestly, if you didn’t know that a triangle has 3 sides, you may need to review your geometric shapes before you take on this Pythagorean Theorem recipe.)Length of Sides A and B – Sides A and B are the two shortest sides on the triangle. The leftover length for the longest side is the hypotenuse. A and B can be the same length, but they are not longer than the hypotenuse.
Recipe Directions:
Really, the directions for the Pythagorean Theorem would be the formula. A2 + B2 = C2
Plug in the length of sides A and B into the variables for A and B in the formula. C is the length of the hypotenuse, or the long side of the triangle. If A was 3 and B was 5, you would have: 32 +52 = C2
Now you square A and B to get: 9 + 25 = C2
If you add 9 and 25, you get: 34 = C2
Now you know that C2 is equal to 34. So, to solve for C, you need to take the square root of both C2 and 34. The square root of C2 is C and the square root of 34 is 5.83.
Now we know that C = 5.83. So your right triangle has a hypotenuse of 5.83.
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