Let’s talk about triangulation in the sense that I became familiar with it –

As keen birders, we would often hear a bird calling from a tree, but try as we might we couldn’t get our binoculars onto it.

We would then separate and each point to the source of the sound. By figuring out where our pointing fingers intersected, we could usually spot the bird.

We would use the same technique to locate a cricket in the house that was driving Helen crazy with its loud chirping.

The same principle can be used to measure distance. Let’s say we have a telescope pointing at the highest level of the tree. We measure the distance from tree to telescope (say, 100m) and we measure the angle at which the telescope is tilted (say 15 degrees).

Now we have a right angled triangle of which we know the base and the angle, so we can calculate the height using the tangent of the angle, which in this case equals 0,27.

We used to look up tangents of angles in a book of tables, but now we simply use Google. In this case Google “Tangent 15 degrees”.

Surveyors use theodolites to measure height in a similar way. The theodolite measures the two angles and the distance is measured between the two measuring points using a surveyor’s wheel

Then they have a triangle for which they know the base and the two base angles so they can determine the height.

That’s how the height of Mount Everest was first determined, but it took a lot of measurements tested against one another to come up with a fairly accurate solution. Now we have satellites, GPSs and the like to achieve even greater accuracy, but they still rely on the basic trigonometry taught in Grade 10.

The term triangulation now has a much broader meaning, which can be summarised as comparing more than one measurement to determine a result. So, it can, for example, mean the same measurement carried out by several people, several measurements made by the same person, and many other approaches to problem solving.