How tall is that Pyramid?

Look back on all of your years of formal education and you are bound to recall some vivid learning experiences. For me, it was this story, related to us by my high school teacher as he introduced us to trigonometry.

Ancient Egyptians used a simple method to measure the height of their pyramids. They would drive a stake into the ground and using its height as the radius they drew a circle around it in the sand. Then, with an observer following the advancing shadow of the pyramid, a marker was placed in the sand at the tip of the pyramid's shadow at the exact moment when the shadow of the stake touched the edge of the circle that had been drawn around it. At that instant, it was obvious that the length of the pyramid's shadow plus half the length of one side of its square base was exactly equal to the height of the pyramid.

The concision and lucidity with which a relatively complex principle could be so simply and so dramatically demonstrated, made a profound impression on me. Not before and never since, have I experienced anything like it.