Similarity - Practice

Although similarity rules have been known since much before Thales of Miletus (Greece, 6th century BC), he is famous because he measured the Great Piramid of Gyza using the laws of similarity of triangles. Let's see how he did it:

First, he drew a circle whose radius equalled his height on the ground, and he waited until the shadow of the piramid touched the circumference, or, also, until both shadows of Thales and the piramid matched up. Then, he marked the point where the shadows had coincided, and he measured the length of the side of the piramid and the distance from the middle to the point.

At this point, let's analize what he did. We have named the different lengths with letters. So, the height of the piramid is h, its side l, Thales' height is b, and c is the distance between the point of the shadows and the side of the piramid. We have two triangles, with a right angle and a common one. Now, let's replace the letters for the previous measuring, and that's all: the height of the biggest piramid in the world.