# One of the largest issues in ancient mathematics was accuracy—nobody had calculators that went out t

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 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 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.
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Step 1
The problem of accuracy arises when calculations involve repeating or non-terminating decimals. trigonometry allows us to use ratios like sin, cos, or tan to accurately represent values in ratio form that can be further used for new calculation which allows more accurate results. There is a Pythagorean theorem too that helps us represent one side of the triangle in form of others using the formula ${c}^{2}={a}^{2}+{b}^{2}$ where c is hypotenuse at the right angle.
Step 2
So, there are many uses of trigonometry in various fields to accurately represent larger repeating and not terminating decimals.