In class, we discussed how Thales measured the distance of a ship from shore using two congruent triangles (p. 93 #3.1(b)). He could have used an alternative method with a similar tool, where the distance could be computed using similar right triangles instead of congruent triangles.
For this method, suppose that Thales observed the ship from the top of a lookout tower; say of height h, and his tool had two legs forming a right angle, so that he could mark off the point E where the line of sight with the ship intersects the leg of the tool that is parallel to the ground, as in the picture below:
(Eye & observer)
E (Point on rod)
Sea level
B (Ship)
4 (Base of tower)
Using the diagram, what are the similar triangles Thales could use in this situation? b) Set up and explain the proportional relationship that would give the distance of the ship to the shore. (Write down an equation using the variables from the diagram and explain it using a sentence or two.)