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Question: 31 while thales was in egypt plutarch claims thales was...

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3.1 While Thales was in Egypt, Plutarch claims Thales was able to determine the height of the great pyramid by measuring the length of its shadow and comparing to the shadow of a known stick. Suppose the shadow of the great pyramid extends 200 cubits past its edge at the same time that a 2 cubit pole casts a 3 cubit shadow. The base of the great pyramid is 440 cubits, so what is its height?

3.2 Eudemus attributes to Thales a method for determining the distances of ships from the shore. A common interpretation of this is that Thales method consisted of similar triangles while standing at the top of a tall tower on the sea shore. Suppose Thales is at the top of a 100 foot tower and sights a ship in the distance that lies along the edge of a right triangle 1.5 feet high and 6 feet base. How far is the ship from the tower?
AC DF BC EF BC EF The following two problems attributed to Thales can be solved using similar triangles. It is speculated tha
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