Indirect Measurement

The ancient Greeks were the first people to start proving their ideas in math. This allowed them to make broad theories about the nature of all things of a certain type instead of a single thing. For example, the Egyptians or Babylonians might know about the triangles they have measured, but the Greeks would try to make theories such as the Pythagorean theory which applied to all triangles of a certain type.
This kind of knowledge, which applies to all things of a type can be used for indirect measurement. In this example, you are trying to find the hight of the large pole from that of the short one. You know the hight of the short one (1 meter) and you know the length of its shadow (1 meter
, you also know the length of the shadow of the long pole (100 meters).

To solve this, first use the Pythagorean theorem to find the length of the hypotenuse of the small triangle. In this case it is the square root of 2. you then make a ratio of the leg of the large triangle to that of the smaller one. (100:1) You then apply this ratio to the length of the upright leg of the small triangle that you know(100:1=X:1). X is the value of the upright leg of the larger triangle. This is an example of indirect measurement, deducing things about the unkown figure based on known relationships to the measured and known figure.