The Pythagorean theorem deals with the lengths of the sides of a right
triangle. The theorem states that: The sum of the squares of the lengths of the legs of a right
triangle (\’a\’ and \’b\’ in the triangle shown below) is equal to the
square of the length of the hypotenuse (\’c\’). Related Links: – Dr. Math Archives
When would I use the Pythagorean theorem? The Pythagorean theorem is used any time we have a right triangle, we know the length of two sides, and we want to find the third side. For example: I was in the furniture store the other day and saw a nice entertainment center on sale at a good price. The space for the TV set measured 17\” x 21\”. I didn\’t want to take the time to go home to measure my TV set, or get the cabinet home only to find that it was too small. I knew my TV set had a 27\” screen, and TV screens are measured on the diagonal. To figure out whether my TV would fit, I calculated the diagonal of the TV space in the entertainment center using the Pythagorean theorem: So the diagonal of the entertainment center is the square root of 730, which is about 27. 02\”. Sounds like my TV should fit, but the 27\” diagonal on the TV set measures the screen only, not the housing, speakers and control buttons.
These extend the TV set\’s diagonal several inches, so I figured that my TV would not fit in the cabinet. When I got home, I measured my TV set and found that the entire set was 21\” x 27. 5\”, so it was a good decision not to buy the entertainment center. The Pythagorean theorem is also frequently used in more advanced math. The applications that use the Pythagorean theorem include computing the distance between points on a plane; converting between polar and rectangular coordinates; computing perimeters, surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes. One of the most common applications of the Pythagorean theorem is in the distance formula. To find the distance between between two points, the distance formula states: in the formula stands for \”difference between,\” so. To see how this uses the Pythagorean theorem, square both sides. Then we have: Can you figure out the right triangle that this describes? Related Links: – Dr.
Math Archives – Dr. Math Archives – Dr. Math Archives How can we prove the Pythagorean theorem is right? There are several different ways of proving the Pythagorean theorem. Here\’s one way: Let\’s start by looking at a square whose side length is (a+b). We can mark a point on the side that divides it into segments of length a and b. Here are three examples, using different lengths for legs a and b: Inside the blue square let\’s construct a yellow square of sidelength c. Its corners must touch the sides of the blue square. The remainder of the space will consist of four blue congruent abc triangles. Here it is for our example squares: In each case, the area of the larger blue square is equal to the sum of the areas of the blue triangles and the area of the yellow square. and the area of a triangle is 1/2(base)(height), we can write the equation: Now subtract the 2ab from both sides of the equation, and we have the Pythagorean theorem: Related Links – Dr. Math Archives – Dr. Math Archives For many more links, for the exact phrase: Pythagorean theorem. And browse related problems in the 1) Road Trip: Letвs say two friends are meeting at a playground.
Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go – he can follow the roads getting to the park – first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras\’s theorem to calculate the distance you will get: 5 Miles. = C Walking through the field will be 2 miles shorter than walking along the roads. 2) Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras\’ theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won\’t tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won\’t tip. What will be the length of the ladder required by the painter to complete his work?
You can calculate it using Pythagoras\’ theorem: 5. 3 m. = C Thus, the painter will need a ladder about 5 meters high. 3) Buying a Suitcase: Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using Pythagoras\’ theorem. It is calculated this way: 4) What Size TV Should You Buy? Mr. James saw an advertisement of a T. V. in the newspaper where it is mentioned that the T. V. is 16 inches high and 14 inches wide. Calculate the diagonal length of its screen for Mr. James. By using Pythagoras\’ theorem it can be calculated as: 21 inches approx. = C 5) Finding the Right Sized Computer: Mary wants to get a computer monitor for her desk which can hold a 22 inch monitor. She has found a monitor 16 inches wide and 10 inches high. Will the computer fit into Maryвs cabin? Use Pythagoras\’ theorem to find out: 18 inches approx. = C Practice Ideas Now write your own problem based on a potential real life situation.