prize7-6, Exercise 1: Triangulation explained

Model answer (check the details):

"Suppose you want to know how far away a church tower is without walking to it. Measure a straight line along flat ground, say 1 kilometre, as carefully as you can. That is your baseline. Stand at one end and measure the angle between the baseline and the tower; do the same from the other end. Now you know one side of a triangle and two angles, which is enough to work out the other two sides by geometry. The distance to the tower is one of them.

Now use the tower's side as the base of a new triangle to a hill farther on, and keep going. A chain of triangles can cover a whole country, with only one or two baselines measured on the ground. Errors are checked by measuring a second baseline far away and seeing whether the calculation agrees."

Diagram in words: a row of triangles sharing sides, like a zig-zag, across the land.