Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle Coursework Aim To investigate the relationships between the lengths, perimeter and area of a right angle triangle. Pythagoras Theorem is a² + b² = c². 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side of a right angled triangle. So the (smallest number)² + (middle number)² = (largest number)² The number 3, 4 and 5 satisfy this condition 3²
through the event of the Triangle Shirtwaist Company Fire. The question being investigated is: to what extent did the Triangle Shirtwaist Company Fire catalyze progress for American laborers? The investigation includes the evaluation of labor unions both prior to and following the Triangle Shirtwaist Company fire. Legislation following this notorious event will also be analyzed in order to properly determine the extent to which this event catalyzed progress for the workers’ rights movement, and its overall
measure the distance of one side of a right angle triangle, (usually known as either a, b and c or side1, side2 and side3) fit the rule a2 + b2 = c2 then the combination of those numbers is a Pythagorean triple. The concept is only correct when the triangle used is a right angle triangle because there must be a hypotenuse across from the right angle. The demonstration used consists of three triangles each of them use positive integers, are right angle triangles and they all fit the rule a2 + b2 = c2
contribution he made are the Pythagorean triples which are three positive integers that follow the a2 + b2 = c2 pattern (Wikipedia , 2013). When a triangle fits into this mold, they are referred to as Pythagorean Triangle (Wikipedia , 2013). Examples would be, 3,4,5 and 5,12,13. When those sets of numbers are seen it can be assumed that the triangle is a right triangle so you can go forth and using the Pythagorean Theorem to solve it. To get a triple set, you need to use Euclid’s formula (Wikipedia , 2013)
Trigonometry Trigonometry uses the fact that ratios of pairs of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right- angled triangle. The term trigonometry means literally the measurement of triangles. Trigonometry is a branch of mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and
Mathematics contributes to everyday life in some way or another. Some situations are simpler than others. Someone may just have to use simple addition or subtraction in paying his or her bills. Or someone may even have to use more complex math like solving for a missing variable in an equation to figure out the dimensions of a building. Mathematics will always be used in everyday life. Some theories and algorithms are more important or used more often than others. Many mathematicians have developed
Around Two thousand five hundred years ago, a Greek mathematician, Pythagoras, invented the Pythagorean Theorem. The Theorem was related to the length of each side of a right-angled triangle. In a right-angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the sum of the squares on the other two sides. (148, Poskitt) To know more about this famous theorem, we can look at the other forms of the Pythagorean Theorem, such as it can also be written as c^2-a^2=b^2
who is immortalized through his genius in the field of mathematics, or more specifically and more widely known the Pythagoras Theorem. A revolutionary theorem, which he created alone, which allows one to uncover the length of the missing side of a triangle by utilizing the other two sides. However, this theorem was not the only thing that Pythagoras was remembered for. In fact he is remembered for his philosophies, childhood, secret life and society, and influential adventures. The man, Pythagoras
Math Fencing Project I have to find the maximum area for a given perimeter (1000m) in this project. I am going to start examining the rectangle because it is by far the easiest shape to work with and is used lots in places (most things use rectangles for design- basic cube .etc). To start with what type of rectangle gives the best result. A regular square or an irregular oblong? I start by having 4 individual squares. [IMAGE] [IMAGE] [IMAGE] [IMAGE] [IMAGE][IMAGE]
perimeter of 1000 metres of fencing. I then worked out the areas of each shape using known mathematical formulae and techniques such as Pythagoras' theorem to calculate the sides of right angled triangles; using trigonometrical functions (sine, tangent and cosine) to calculate either angles or sides of triangles constructed. Sometimes there are no known exact formulae for working out the area of certain shapes such as octagon and more complex polygons. In such cases, given shapes are split
Beyond Pythagoras - Mathematical Investigation 1) Do both 5, 12, 13 and 7, 24, 25 satisfy a similar condition of : (Smallest number)² + (Middle Number)² = (Largest Number) ² ? 5, 12, 13 Smallest number 5² = 5 x 5 = 25 Middle Number 12² = 12 x 12 = 144+ 169 Largest Number 13² = 13 x 13 = 169 7, 24, 25 Smallest number 7² = 7 x 7 = 49 Middle Number 24² = 24 x 24 = 576+ 625 Largest Number 25² = 25 x 25 = 625 Yes, each set of numbers does satisfy the condition.
Theorem 1-3 Congruent Complements Theorem If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. Theorem 2-1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Theorem 2-2 Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Theorem 2-3 Polygon Interior Angle-Sum Theorem The sum of the measures of the interior angles of an
find the area of irregular triangles and a regular triangle, irregular quadrilaterals and a regular square, this will prove whether irregular polygons are larger that regular polygons. Area of an isosceles irregular triangle: ======================================== (Note: I found there is not a right angle triangle with the perimeter of exactly 1000m, the closest I got to it is on the results table below.) To find the area of an isosceles triangle I will need to use the formula
And these tablets are believed to date about 1000 years before Pythagoras. And the Babylonians are not the only ones!According to Eric McCullough & Brian Deitz the Egyptians knew that a triangle with sides 3, 4, and 5 make a 90 degrees angle, and they also used a rope with 12 evenly spaced knots that they used to build perfect corners in their buildings and pyramids. In another article, titled The History of the Pythagorean Theorem, ancient
Drain Pipes Shape Investigation Introduction A builder has a sheet of plastic measuring 2m by 50cm, which he uses to make drains. The semi-circle is the best shape for a drain. Prove this. I will prove this by comparing its volume to that of other shapes. On older houses there are semi-circular drains but on newer houses there is fancier ones like pentagon shapes. Is this because they are better or is it simply for design? To find the volume of a 3D object I have to find the
fitting 4 triangles inside each triangular surface of an icosahedron; which is one of the five solids created by the ancient Greeks. When considering a icosahedron, or any regular polyhedral for that matter, we have the following formulas to consider: 1. V = 10υ2 + 2 2. F = 20υ2 3. E =
Using Tangrams To Explore Mathematical Concepts Representations have always been a very important part of teaching mathematics. The visuals and hands on experiences help to aide the teachers by assisting them in relaying important topics and concepts to the students. By having a representation, the students are more likely to remember what they have learned, and recall the lesson when it comes time to take a test or do their homework. Within mathematics, many different manipulatives are
sides and angles of a triangle, such as Special Right Triangles (30, 60, 90 and 45, 45, 90), SOHCAHTOA, and the Law of Sines and Cosines. These methods are very helpful. I will explain how to use all three of them with examples at the end. The first example, Special Right Triangles, is used only with right triangles. To use this method, you need to have angle measures of 30, 60, and 90, or 45, 45, and 90. There is a "stencil" that goes with these degrees. In the 30-60-90 triangle, the side opposite
complete the race? I would like to investigate two different models one being a right-angled triangle and the other being isosceles triangle. When investigating the isosceles triangle, an equilateral triangle would be investigated because as the length of the isosceles triangle will all equal, it becomes an equilateral triangle. I would first of all investigate the right-angled triangle. Model 1: Right-Angled Triangle C [IMAGE] A B [IMAGE] PREVAILLING CURRENT AT A SPEED OF 2 MS-1
Physics problems can be solved and worked through many different ways. For example, for the second half of the problem (when we used d = d0 + v0t + ½ at2), we could have also used trigonometry to find the height, since we already know the base of the triangle (half the distance) and the angle. Despite enrolling late and still trying to figure everything out, I still participated in the class a bit, having asked and answered a few questions of Piazza. For example, I helped another newly enrolled student