Hello,

I am having trouble finding any answer to this question using my source. I can see from other course hero answers that people mention the Principles of similar triangles but I honestly did not read anything about that in this source. I feel my answer makes some sense but I am not totally sure. If you could check or help add to this I would really appreicate it.I am using what I can from Section 7.2 but am unsure if my answer makes sense.

The required reading was from this source: https://openstax.org/details/books/algebra-and-trigonometry-2e

Section 7.1 Angles

Section 7.2 Right Triangle Trigonometry

Section 7.3 Unit Circle

Section 8.1 Graphs of the Sine and Cosine Functions

Section 8.2 Graphs of the Other Trigonometric Functions

Section 8.3 Inverse Trigonometric Functions This is the question:

Original Question:

One of the largest issues in ancient mathematics was accuracynobody 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.

This is the best answer I can give:

Given two similar triangles, where one triangle has small accurately determined measurements and the other triangle has larger measurements but at least one known measurement, the other two measurements can be deduced using the principles of right triangle trigonometry.

Trigonometry deals with the relationships between angles and sides in a triangle. By applying fundamental trigonometric ratios, such as sine, cosine, and tangent, we can establish connections between the angles and sides of a triangle.

In the case of similar triangles, we can utilize these trigonometric ratios to find the unknown measurements. For instance, let's consider two similar right triangles. If we know the length of one side in the smaller triangle and the corresponding angle, and if we have the value of at least one side in the larger triangle, we can set up a proportion using the trigonometric ratios to determine the lengths of the other two sides.

By utilizing the available information, including the known accurate measurements and the principles of right triangle trigonometry, we can ascertain the values of the missing measurements in the similar triangles.