The Pythagorean Theorem
Using real-life examples in teaching this concept
The Pythagorean Theorem was developed by the Greek Philosopher Pythagorus and is used in every day situations. These tips can ease the normal anxieties felt by students.
The words "Pythagorean Theorem" can sound incredibly intimidating to typical middle school math students. What students may not initially realize is that the Pythagorean Theorem is executed in various daily situations, some that students may have already experienced without realizing it. Introducing this concept using real life examples can help set the stage for easier problem solving and a deeper understanding and can hence help students appreciate the reasons why it’s essential to learn this concept at all.
The Pythagorean Theorem consists of the following: The sum of the squares of two legs of a right triangle is equal to the hypotenuse squared.
For example, if one of the legs is 6 inches and the other leg is 7 inches, we can calculate how long the hypotenuse, or the third leg is. Let a = 6, b=7, and c= the length of the hypotenuse. (6)^2 + (7)^2 = c^2. 6*6=36, and 7*7=49. Thus, 36 + 49 = 85. So, the square root of 85 is approximately 9.2 inches. Therefore, we just calculated the length of the hypotenuse using this theorem.
The following consists of real life applications to introduce to students which can greatly ease their anxieties and further promote their learning.
Baseball Diamond
If the teacher asks students how many of them play baseball or enjoy baseball, the majority of boys in the classroom will more than likely raise their hands. The teacher can utilize this concept by using an overhead transparency, chalkboard, or other advanced technological device. In a baseball diamond, the distance between each of the three bases and home plate are 90 feet and all form right angles. If a teacher draws a line from home plate to first base, then from first base to second base and back to the home plate, the students can see a right triangle has been formed. Using the Pythagorean Theorem, the teacher can then pose the question, "How far does the second baseman have to throw the ball in order to get the runner out before he slides into the home plate?" (90)^2 + (90)^2 = c^2, or the distance from home plate to second base. 8100 + 8100 = 16,200. The square root of 16,200 is approximately 127, so the second baseman would have to throw it about 127 feet.
Height of a Building
Firemen, construction workers, and other workers often rely on the use of ladders in their line of work. They make use of the Pythagorean Theorem in various situations. For example, the height to a second story window may be 25 feet, and a window cleaner may need to put the ladder ten feet away from the house in order to avoid the bushes or flowers. How long of a ladder does the window cleaner need in order to achieve this task? (25)^2 + (10)^2 = c^2, or the length of ladder needed. 625 + 100 = 725. The square root of 725 is approximately 27, so the window cleaner would need a ladder 27 feet long.
Two friends meeting at a specific destination
Let’s say Bob and Larry are meeting at Blockbuster on the corner of Park and Pleasant Street. Presently, Bob is on Park Street to and is 8 miles away. Meanwhile, Larry is on Pleasant Street 7 miles away. How far away are they from each other? (8)^2 + (7)^2 = distance between Bob and Larry. 64 + 49 = 113. The square root of 113 is approximately 10.6. Thus, this is how far apart Bob and Larry are from each other.
Ramp of a moving truck
The height of a moving truck is 4 feet. The distance from the bottom edge of a ramp on the ground to the truck is 6 feet. How long is the ramp? (4)^2 + (6)^2 = length of ramp.
16 + 36 = 52. The square root of 52 is approximately 7.2, which is the length of the ramp.
Measurement of TV
Television sets are generally measured diagonally, thus classifying them as 13 inches, 27 inches, 36 inches, and so forth. Suppose we want to purchase an entertainment center, but it only holds enough room in it’s cubicle for a 27 inch TV set. We initially know that the length of our TV is 15 inches, and the height of our TV is 12 inches. Will our TV be able to fit into the cubicle? (15)^2 + (12)^2 = 369. The square root of 369 is approximately 19.2 inches. Therefore, our TV will fit with plenty of room to spare.
Introducing these real-life situations to students will ease their mind on learning this powerful concept. The name doesn’t have to be intimidating once students appreciate the meaning behind the Greek Philosopher Pythagorus’ theory. The Pythagorean Theorem is involved in many other everyday uses as well, which will help students develop a thorough understanding of the fascinating complexities behind the right triangle.
