The story is told of a Greek traveller who was asked how tall the great pyramid was. Nobody knew. It was far too large to climb with a measuring line, and there was no way to reach the top from the outside.
He pushed a stick upright into the sand, waited, and measured two things: the length of the stick's shadow, and the length of the pyramid's.
Suppose the stick stands two units tall and throws a shadow three units long, while the pyramid's shadow reaches two hundred and ten. The sun is so far away that its rays arrive at the same angle everywhere in that field, so the stick and its shadow form a triangle with exactly the same shape as the pyramid and its shadow — a small one and a large one, otherwise identical.
Whatever the stick's height is compared with its shadow, the pyramid's height must be compared with its own shadow in the same way. Two to three, and two hundred and ten to one hundred and forty. The pyramid is a hundred and forty units tall.
Notice what he never had to know: the length of the pyramid's sides, the size of its base, or how it was built. Two shadows and one stick were the whole of it.
The method costs nothing and needs no instrument. It is still used: a forester measuring a tree, a student measuring a school building. The only requirement is that both shadows be measured at the same moment, because the angle changes through the day.