Water Tower Geometry

This year my school obtained a lease on an overgrown orchard adjacent to our back yard. The new land has offered a number of great opportunities for instruction. A disused water tower, located a couple meters past the new rear gate, has piqued my attention this week.

20140923_094622Today, I took my grade 12 math class down to the tower and asked them to determine the height of the small platform you can see near the top. We brought along a meter stick and a white board.


The students decided to think of the challenge in terms of coordinate geometry. They were able to define the problem, draw the indicated line, and outline a solution: determine the equation of a line-of-sight between someone on the ground and the platform. Unfortunately they got stuck at this point, and I needed to remind them that they could use two points to define a line — that was enough for them to establish a procedure whereby one sighted the platform while sitting, and another moved about until the top of her head was in the line of sight of the sitting student.


The students took characteristically incautious measurements, so I went back and re-did the experiment myself. Here is a photo from my attempt.


I found a height of about 20 meters, which jives with my expectations. I’m looking forward to returning to the tower after a forthcoming unit on trigonometry to see if the students can do a better job using angular measure. I might even get them to use my sextant…



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