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

###### Question details

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?