Special right triangles

At about twenty centuries ago there was an amazing discovery about right angled triangles: “In a right angled triangle the square of the hypotenuse is equal to the sum of squares of the other two sides.” It is called Pythagoras Theorem and can be written in one short equation: a²+b²=c² where c is the longest side of triangle and a and b are the other two sides. Pythagoras was born in the island of Samos in 570 BC in Greek in the eastern Agean. He was the son of Mnesarchus and his mother's name…

We can easily convert this into Cartesian form by replacing z by x+iy |(x+iy)-(-3 +2i)|=5 |(x+3) + i(y-2)|=5 √(〖(x+3)〗^2+〖(y-2)〗^2 ) =5 or 〖(x+3)〗^2+〖(y-2)〗^2=25 Which is the exact form of a Cartesian equation of a circle with a center of (-3, 2) and a radius of 5 We could check if a particular point lies on the circle Ex. z2=1-3i Substituting into the equation of the circle, with z replaced by z2=1-3i |(1-3i) - (-3 + 2i)|=5 |4-5i|=5 √(4^2+〖(-5)〗^2 ) =5 41=5, which is not true, thus z2 does not…

While it is necessary to delegate different tasks to team members, leaders also possess the responsibility of their team as a whole. While my Robotics team was revising our robot for the VEX Robotics Mid-Atlantic Championships, I made sure to keep track of the team’s progress in the engineering notebook, as well as supervise the work of my fellow team members. At Governor’s School, I will make sure to collaborate and contribute ideas, as well as provide leadership skills such as guidance,…

The theorem used to find the hypotenuse, adjacent, or opposite sides of a triangle is also used in Euclidian Geometry. “A” squared plus “B” squared equals “C” squared is the formula used in the theorem. For example, we are given two numbers in the sides of a triangle; if we are given the adjacent and opposite sides, and we must figure out the hypotenuse, we will be required to use the Pythagorean Theorem. The two numbers…

in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It does not tell us exactly which right triangle to draw. There are many right…

non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic lemmas, one is on the fact “Among all the pedal’s…

their physiques, the skirts create a strong core that allows for a slightly altered pose without the threat of instability. This makes her strong and grounded, but not weighed down or heavy. She stands with her weight slightly shifted to sit in her right hip, which brings the viewer to look up the figure. Her face appears serene, staring out with a soft gaze. The flowing fabric and tranquil expression create a general feeling of gentleness and calm about her. Faustina the Elder is comprised…

The country of natat mortem (death swims), is under the sea located in the bermuda triangle along the tropic of cancer, northwestern hemisphere, with the coordinates of 25.0000 N and 71.0000 W, elongated east to west. The climate is tropical and extremely hot throughout the year, in fact the water is in the constant state of boiling due to the tropical temperatures. Though it seems there should be no survival in the hot temperatures the genius supreme leader esther falokun developed pod like…

Swami Vivekananda said “Every change is being forced upon us.” In Tally’s world no words could be more true. Pretties and Specials are the second and third books in the Uglies series. Within the trilogy the story follows Tally, a young girl who finds out what is truly happening in her society. In Tally’s futuristic city people undergo an operation on their sixteenth birthday to become a “Pretty” the operation alters their looks and their brains. During the operation a lesion is put in everyone’s…

city and works at a place called special circumstances. David is the leader of a secret city called the smoke; it was formed by David’s parents who are runaway doctors from the big city consisting of: New pretty town and Uglyville. The rangers take care of the forest and all of the plants outside of the city. They live in their own city by themselves. The Uglies is the beginning of a very long story, starting with Tally Youngblood wants to become pretty but special circumstances and Dr. Cable…