The "Surveying Challenge" consists of two parts.

Challenge One

You are behind a line on the ground and cannot pass, reach or stretch beyond. On the ground next to you is a small spot, and at some unknown distance from you is a small pot. Your task is to determine the distance from the spot to the pot.

The only materials you have are those typically found in a house. Tape measure or ruler, pencil, paper, string, etc. are all allowed, but nothing exotic such as a theodolite or sextant.

You don't know the size of the pot.

Challenge Two

As per challenge one, except now there are two small pots, and you have to determine the distance between them.

Discussion

Measuring the height of a tree or building is a classic problem from trigonometry. This goes a stage further. Now you don't know the distance to the pot, or the size of the pot. Suddenly you appear to have too many unknowns and not enough "knowns".

However, not only is this possible, it's possible to do it without a scientific calculator.

This is one of the many Enrichment tasks on this site.

CategoryMaths
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