University: University of the people
Course: College AIgebra (MATH 1201 )
Discussion forum unit 7
One of the largest issues in ancient mathematics was accuracy4nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment, which can be found at https://www.famousscientists.org/eratosthenes/, relied on the fact known to Thales and others that a beam of parallels cut by a transverse straight line determines equal measure for the corresponding angles. Given two similar triangles, one with small measurements that can be accurately determined, and the other with large measurements, but at least one is known with accuracy, can the other two measurements be deduced? Explain and give an example
The similarity of triangles gives rise to trigonometry.
How could we understand that the right triangles of trigonometry with a hypotenuse of measure
proportions between sides of two triangles, and these proportions allow for the calculations of which we are speaking here. The similarity of triangles is the foundation of trigonometry.
Your Discussion should be a minimum of 250 words in length and not more than 750 words.
SAMPLE SOLUTION:
According to PhD Essay "The growth of contemporary trigonometry shifted in the western Age of Enlightenment, starting with 17th 3 century math and reaching its contemporary type with
"trigonometry,= implying "triangle measuring,= from triangle + to measure, = (PhD Essay, n.d., para. 3).
The chord of an angle subtends the arc of the angle. And to talk of ancient Greek mathematicians used the chord. And when there is an arc on a given circle, the chord is the line that subtends the arc. A chord's perpendicular bisector transverses the Centre of the circle and bisected angle (PhD Essay, n.d.).
According to PhD "One half of the bisected chord is the sine function also known as the "half 3 chord=. As a result of this relationship, several trigonometric identities and theorems that are known at present were also known to Greek mathematicians, however in their equivalent chord form,= (Essay, n.d., para. 9).
There is no trigonometry in the works of Euclid and Archimedes, there are theorems presented in a geometric method that looks like a particular trigonometric law. The theorems on the length of chord are applications of the law of sines and also Archimedes' theorem on broken chords is also similar to rules for sines of sums and differences of angles (PhD Essay, n.d.).
According to Abramson it says "Given a right triangle with an acute angle of t, the first three trigonometric functions are listed. Sine sin t = opposite /hypotenuse Cosine cos t = adjacent/ hypotenuse Tangent tan t = opposite /adjacent A common mnemonic for remembering these relationships is SohCahToa, formed from the first letters of "Sine is opposite over hypotenuse, Cosine is adjacent over hypotenuse, Tangent is opposite over adjacent.= For the triangle shown in Figure 1, we have the following. sin t = y /1 tan t = y / x cos t = x /