“When are we ever going to use this in real life?”

Every teacher has heard this at one time or another. Math teachers hear it a lot.  Grant Union High School geometry students recently got a chance to find out.

The students had just finished studying a section about similar triangles – triangles that have the same shape but are different sizes.  The cool thing about similar triangles is that all the sides are proportional.  If one side of the bigger triangle is three times as big, so are the other sides.  Students used this concept to find the height of the flag pole. 

With the aid of a mirror lying on the ground, students, working in teams, made sure they could see the top of the pole in the mirror. They then measured the distance from the pole to the mirror (b), the distance from the mirror to their feet (c), and the distance from their feet to their eyes (d).

The height of the flag (a) compared to the student’s height (d) is exactly the same as the distance to the flag pole (b) compared to the distance to the student (c).

The final results gave us a range of heights from 25 feet tall to almost 60 feet. 

After some discussion about possible reasons for different answers (which included where in the mirror the top of the pole was, or leaning forward to see the mirror, or even some problems with using meter sticks to measure feet), we decided that the flag pole is about 45 feet tall. 

Unfortunately we haven’t been able to find anyone at GUHS who knows exactly how tall the flag pole really is. If you know, please let us know. We’d like to check our answers.

– Rich Lallatin