A few days ago, my Honors Precalculus students finished up their study of trigonometry. In this activity, they used what they learned to measure the height of the library on our campus. I’ve done this activity before with my Geometry students and a flagpole (see this post). The girls needed to measure the angle of elevation from the student observer to the library roof, and the horizontal distance from the front of the library to the student. Then, using the tangent function, they can calculate the vertical height of the library:

Here’s a shot of the sextant we made and the geometry involved in calculating the angle of elevation:

It was beautiful day – sunny and in the mid-60s – so nobody complained about going outside! I divided the class into three groups, and each group took their measurements from a different spot along the front of the building.

Measuring the horizontal distance

Measuring the angle of elevation

All three teams came up with fairly consistent results: between 27.5 feet and 29 feet!

I’ve been teaching math long enough to know that a year from now these girls won’t remember very many of my wonderful lectures, but hopefully they won’t forget the day they used trigonometry to figure out how tall their library is.

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You could also measure the shadow of the building, then measure the shadow of the measuring device (yard stick or ruler), then solve for the missing variable (height of building). Might be a fun comparison to this activity to see the accuracy of different methods.

Thanks for the suggestion! I’ll definitely add that to this activity next time we do it.