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In particular we show that if the similar triangles have 120 degree angles at their apex, then recursive application of this pseudo Napoleon's construction will, in the limit, construct a triangle congruent to Napoleon's.
Instead, the setter can make use of similar triangles to determine the area of Triangle B, which is about 22.
For example, there are 4 instances of pairs of similar triangles in the configuration, but they are considered as a single one since each can be derived from the any other with a cyclic permutation of the point labels (see Figure 5).
The cases that do not appear in the list are either cannot occur or lead to similar triangles.
Wikipedia's entry about the history of trigonometry is there for all to read (on the website, several reliable sources are referenced at the bottom): "Pre-Hellenic societies such as the ancient Egyptians and Babylonians lacked the concept of an angle measure, but they studied the ratios of the sides of similar triangles and discovered some properties of these ratios.
In particular, they focused on identifying similar triangles to determine the length of the height (figure 13).
For example, teachers explain that light travels in a line or that the shadow cast by a person is related by similar triangles to that cast by a flagpole.