Similar triangles are just what you need to simulate Thale's indirect measurement of the distance from the shore to a ship offshore. (Perhaps there is a buoy or some other marker that can be sighted from the shore of your beach.) There is a writeup of this in "For All Practical Purposes" text. If that's not handy, here is roughly how it goes (it assumes that where the beach meets the edge of the water is fairly straight):
Sight the object so that the line of sight is perpendicular to the shore (and plant a stick A in the sand at that spot); then walk (pace off) on the edge of the beach in a straight line several yards (say 10), plant a big stick B; continue walking in the same straight line another several yards (say 5), plant a stick C; make a right angle and walk away from the shore in a straight line and as you do so, keep checking to see when you can sight your offshore object in a straight line through the big stick B you planted. When you reach that point, stop and plant your last stick D. If the offshore object is at point P, then right triangle PAB is similar to right triangle DCB, and you have paced off the measurements AB, BC and CD. The ratios (of corresponding legs of the two right triangles) PA/AB and DC/CB are equal, so you can calculate the distance PA from the shore to the offshore object.
You can also use similar triangles to calculate other distance that must be measured indirectly-- have fun and keep cool.
At 4:28 PM 7/7/95, HoxFan wrote: >I teach an intensive summer geometry class in Santa Cruz, CA. It's 4 >hours a day and the kids and I are suffering from the heat. Any >suggestions on what we can do at the beach that I can relate to geometry. >( We are going to start similar triangles on Monday)