How Tall Is The Atrium?

Today it’s raining, which put a dent into plans to go outside to use shadows and similar triangles to measure heights of things near the school, so we used a good rainy day method instead.

To start off, we did some review of similarity, starting with some similar rectangles, and some work on scaling dimensions proportionally. We then looked at some similar right angle triangles, and finally some nested right triangles which will look like what our experiment will use. We got good at figuring out the scale factor, then using it to solve for an unknown side. Once we had those skills back at the top of our minds, we went downstairs and worked on getting some measurements to use for our calculations.

We held a meter stick vertically in our outstretched arm, then lined up the top of the meter stick with the edge of the ceiling and the wall of the atrium.

We measured arm length, and the height of the ruler above our hand, and then the distance from us to the wall, and the height of our eyes, and used that to make similar triangles and calculate the height of the atrium.

We had 3 groups all working at a different distance from the wall, so each group would have different information, and we were curious to see how close the answers would be.

We got back to class and did our calculations. We had a lot of variability in our answers, from 6 meters to 14 meters. We used some estimates of how tall one classroom is, and then extended that to 2 floors, and saw that the real answer is likely somewhere in between those values.