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3. The attempt at a solution

I can't figure out how thales found the measurement of the length of this triangle without trigonometry since the sine and cosine ratios were not worked out until the 14th century I think. In any case, they certainly weren't known in thales' time. using trig the answer is rather straightforward, but without trig the only method i can think of for obtaining the length of the bottom line of a right triangle is rather crude. what thales could do is redraw the triangle on the beach since if he knew the AB length and the DAC angle he could physically draw the BAP triangle on the beach, although it would be a rather large and crude replica of the real triangle, but that's the only method i can think of.

any help would be greatly appreciated.

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# Length of triangle

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