One of the largest issues in ancient mathematics was accuracy-nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment, that can be found at 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 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for 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.

Question

One of the largest issues in ancient mathematics was accuracy-nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment, that can be found at 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 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for 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.

Faiza Fuller · Accepted Answer

Step 1  Small sized triangle:  Let us consider a triangle ABC with three given sides, as shown in the attached image.  AB=15cm, BC=12cm and AC=8cm  We can measure the three angles with the help of protector and will get the values as shown.  This triangle is small and can easily be drawn and we can measure the three angle A, B and C with the help of protector.  Note: There are three sides given so drawing the triangle is no issue and even we can measure the three angles.  Step 2  Large sized triangle:  Now when we have a very big triangle, for which it is not possible to draw on a piece of paper.  Now there are few things to understand,  Similar Triangles:  The sides of the large triangle are proportional to the three sides of the small triangle, then the three angles of the large triagle will be the same as three angles of the small triangle.  For example we have a triangle PQR, with its side PQ=1500m, QR=1200m and PR=800m then it is obvious we cant

One of the largest issues in ancient mathematics was accuracy-nobody had calcula

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