### Other than those listed in the text, how might the Pythagorean theorem be used in everyday life? Provide examples of each.

## Response 1

Pythagorean Theorem can be used in everyday life in the following ways: Painting a wall Determining the size of a suitcase needed when going on a business trip Finding the right size TV or computer to buy Cleaning a window In this specific example the window is 12 feet off of the ground. There is a bed of flowers beneath the window that extends out 5feet. You have a ladder that is 13 feet and you want to know if this is tall enough to get the job done. To determine if the ladder will extend high enough to reach the window you would: o Look at distance of the window 12ft and o Look at distance of the flower bed 5ft and o Look at height of ladder 13 ft. A^2+b^2=c^2 a and b are the legs 12^2 +5^2 = 144+25=169 169=c^2 13=c So the answer is yes, the ladder is high enough to reach the window to clean it## Response 2

According to the Pythagoras theorem the sum of the squares of two sides of a right triangle is equal to the square of the hypotenuse. E.g. Let one side of the right triangle is a, the other side is b and hypotenuse is given by c. According to the Pythagoras theorem a2 + b2= c2 Everyday uses for the Pythagoras theorem are: What size TV to purchase Length of a ladder need to paint the wall or clean a window Building and home construction: architecture and building construction, particularly in reference to triangular-shaped roofs and gables. The theorem applies only when dealing with right triangles or triangles with a 90-degree angle. Navigation: Cell phones can be traced by way of triangulation. Car navigation systems use this method. Triangulation can also be used in conjunction with a compass to determine one’s geographic location Crime Scene Investigators: Forensic investigators use the Pythagorean Theorem to determine bullet trajectory.## Response 3

The Pythagorean theorem is used in everyday life for finding lengths in right triangles for architecture/constructions, navigation, crime scenes, or projectile trajectory. The obvious one is in architecture/construction making sure the building is built right. People use the Pythagorean Theorem in navigation to locate there position form ancient ways of sailing to modern sailing, all the way to locating space crafts. In crime scenes the investigators can find the path bullets fallowed and blood splatter trajectory. The investigators can determine how close the shooter was from the victim. Archers can use the Pythagorean Theorem to determine the correct trajectory to hit the target and also can happen with the trajectory of missile systems.## Response 4

Other than those listed in the text, how might the Pythagorean theorem be used in everyday life? Provide examples of each. Pythagorean theorem and its uses in day today life: It is used to calculate the diagonal length of the computer screen or a tv as computer and TV’s are measured by their diagonal. For example the width of a computer screen is 12 inches and its height is 10 inches. sqrt912^2 + 10^2) = 15.62 in (approximately) If you want to know the actual dimensions of tv screen size and you know the ratio of sides (16:9 or 4:3) then you can find them from the Pythagorean theorem. For example, take a 42″ TV with a 16:9 ratio, the diagonal is √(16^2 + 9^2) = 18.36 from the Pythagorean theorem. So, the diagonal: width; height ratio is 18:36:16:9. Find width from 42(16/18.36) = 36.6″. The height can be found similarly. It is used in criminal investigations to find the trajectory of a bullet. Geologists use it to calculate the epicenter of earthquakes. It is used in building fences. It is also used in architecture in general. It can be used to find the distance between two cities using a reference point or the magnitude of a vector given its horizontal and vertical components. To find the between two points, the distance formula states: d = square root of triangle x to the second power + triangle y to the second power. The formula stands for “difference between”, so x = x^2 – x^1 and y = y^2 – y^1## Response 5

Other than those listed in the text, how might the Pythagorean theorem be used in everyday life? Provide examples of each. Pythagoras is very well known, considering he published no writing during his lifetime. What we know of Pythagoras has come from other philosophers and historians. Pythagoras was a Greek philosopher and mathematician who is best known for introducing the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is the equivalent of the sums of the squares of the other two legs of the triangle. The theorem is not just a geometric postulate; it also has real world applications Retrieved frpm: http://www.ehow.com/info_8247514_real-life-uses-pythagorean-theorem.html## Response 6

It can be used in baseball to figure out how far a ball was thrown. Say you’re the first baseman and you throw the ball to get the runner, going from third to home, out. Using the equation I plug in the numbers, a baseball diamond is actually a square but it has right angles so we divide the diamond through the middle. This leaves us with a right triangle. Two of the sides measure 90 feet so our equation will read (90)2 + (90)2 = c2. next: C= sq.rt 902 + 902 C= sq,rt 16,200 = 127.28. You will throw the ball 127.28 meters to strike out the runner.## Response 7

According to wikipedia, “the pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides”. The formula for this is a^2+b^2=c^2. For me this theorem can be used when I build sets and huts for my daughter’s dance school. If the our 2 sides are 5ft and 4 ft, then 5^2+4^2 = 25+16 = 41.## Response 8

**1) Road Trip:**Let’s say two friends are meeting at a playground. One friend is located on the south-west corner of playground and other is located on the north-east corner of the playground. There are two ways to go let us see how you can take the help of Pythagoras theorem to calculate the shortest distance between the meeting points of two friends. If you follow a road 3 miles east and then 4 miles north. Your total distance covered will be 3+4 = (7) miles but if you apply the Pythagoras theorem to calculate the distance you will get: (3)

^{2 }+ (4)

^{2}= 9 + 16 = C

^{2}√25 = C 5 Miles. = C So this will save them 2 miles distance.

**2) Painting on a Wall:**Painters use ladders to paint on high buildings and often use the help of the Pythagoras theorem to complete their work. Take for example a painter who has to paint a wall which is about 8 m high. The painter has to put the ladder 6 m away to avoid a rack in between. What will be the length of the ladder required by the painter to complete his work? You can calculate it using the Pythagoras theorem: (8)

^{2 }+ (6)

^{2}= 64 + 36 = C

^{2}√100 = C 10 Mts. = C Thus, the painter will need a ladder 10 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 the Pythagoras theorem. It is calculated this way: (18)

^{2 }+ (b)

^{2}= (30)

^{2}324 + b

^{2}= 900 B

^{2}= 900 – 324 b= √576 = 24 inches

**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: (16)

^{2 }+ (14)

^{2}= 256 + 196 = C

^{2}√452 = C 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 Mary’s cabin? Use the Pythagoras theorem to find out: (16)

^{2 }+ (10)

^{2}= 256 + 100 = C

^{2}√356 = C