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.

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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.

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

watertower

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…

sextant

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