What's the Fuss About Pythagoras?
Jenny is an eighth grade student who loves math. One day, she came home from school and was so excited to tell her sister, Melissa what she learned in Pre-Algebra class. "I learned this cool Theorem that was created by some mathematician with an awesome last name!" Jenny exclaimed. "What is the Theorem called?" Melissa questioned. Jenny thought hard about it and blurted out, "It's the Pythagorean Theorem and it's used to find the length of the side of a right triangle!"
Melissa was eager to hear more. She asked, "How do you know when to use it? Will it always work?" Jenny remembered her teacher telling the class that the Pythagorean Theorem ONLY worked with right triangles. So, she explained this to Melissa. Melissa, a fifth grader, wasn't sure how to determine if a triangle is a right triangle.
Jenny wanted to help her sister understand right triangles so she explained, "A right triangle is a triangle with two legs and one hypotenuse. One of the interior angles of a right triangle must be a right angle. This means that it measures 90 degrees." "Oh, I think I get it!" Melissa replied.
Jenny was determined to make Melissa understand what the Pythagorean Theorem was and how it was used. The Pythagorean Theorem is a^2 + b^2 = c^2. In this equation, a and b are the legs of the right triangle and c is the hypotenuse. You can only use this theorem if you have the length of two sides of a right triangle and are looking to find the length of the third.
Melissa says, "Oh! I think I got it! Let's do a problem together so that I can make sure I understand what you're saying." Jenny grabbed her math textbook and found a problem for them to complete together.
Jenny picked the following problem:
A ramp was constructed to load a truck. If the ramp is 9 feet long and the horizontal distance from the bottom of the ramp to the truck is 7 feet, what is the vertical distance of the ramp to the nearest 10th of a foot?
problem from: http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm
Together, Melissa and Jenny worked on the problem with their calculators in hand. They found out that the vertical distance is about 5.66, which rounds up to 5.7. Jenny said, "See, Melissa! Math is used in real life and now I know why learning the Pythagorean Theorem is so important! I see what the fuss over Pythagoras is all about! Tomorrow, I am going to thank Ms. Scarlata for teaching us the Pythagorean Theorem in Pre-Algebra class!
The images are from:
http://www.analyzemath.com/Geometry_calculators/right_triangle_calculator.html
http://schools.bvsd.org/p12/heatherwood/academics/math/Pages/default.aspx
http://bookbuilder.cast.org/view.php?op=view&book=15398&page=2
http://www.mathguide.com/lessons/Pythagoras.html
http://www.dreamstime.com/stock-photos-stock-photos-two-young-girls-thinking-books-image8413673
http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm
The problem is from:
http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/Pythag.htm
The coaches:
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