Today in geometry, we used trigonometry to estimate the height of a flagpole. First, I made a homemade sextant, using a protractor, some thread, and a piece of paper that I rolled around a pencil and taped to the protractor:

Homemade Sextant

I weighted the thread with four large paper clips. You can see from the picture that the line of sight makes a 50 degree angle with the vertical thread. To estimate the flagpole height, we needed the angle of elevation, which is measured from the horizontal. So, some geometry needs to be applied to figure out the angle of elevation:

Angle of elevation is 40 degrees

Now that we knew what to do, we went outside and measured 10 meters from the base of the flagpole. Then, one of my students used the sextant to sight the top of the pole, while another student read off the angle indicated by the thread:

Sighting the top of the flagpole

The angle was 51 degrees, which meant the angle of elevation must be 90-51 = 39.

So here’s the picture the students drew on the Smartboard:

Figure illustrating the problem

Notice that they realized they had to take into account the height of the person taking the sighting. My other geometry class did the same activity, and they got a result of 9.7 meters. Pretty consistent!

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Thank you for the easy to understand article. Just what I needed.

We have 7 meters measured from the based of the flagpole and 50° from ours sextant. We tried your formulation and we’ve got the measure of the Flagpole 7.6m. Is it correct?

If your sextant reading was 50, then your angle of elevation would be 40. 7tan(40) = 5.9 m. Make sure your calculator is in degree mode!