For this problem, we had to find the height of the HTHCV flagpole by using 3 different methods. The 3 methods we had to use were the Shadow Method, Mirror Method, and Isosceles Method.
Process & Solution
Anatole launched the height of the HTHCV flagpole by proposing a question: "Our fearless leader Tim wants to buy a new flag for the front of the school. He wants the biggest one possible but there are regulations about how large a flag can be. These rules are based off the flagpole. But! We don't know how tall our flagpole is. We've been asking around and no one at HTHCV knows" My first initial guess was that the flag pole was a Minimum of 60 feet and a Maximum of 100 feet. By doing this problem, I was able to learn similarity and what makes two polygons similar. Similarity - When two polygons have corresponding angles and their corresponding sides are proportional.
For the shadow method, you have 3 side lengths which means you use the SSS Theorem. (Side, Side, Side). I first measured my actual height and then we stood near the actual flag pole, and measured how far our shadow was from the flag pole. My actual height is 65" and my shadow height was 96". I then divided 65 by 96 to get the scale factor which was 0.67708333. I then took that number and multiplied it by 660 since that was we got for shadow height of the flag pole, and the final answer I got was 446.875".
Just like the shadow method, the Mirror Method also used the SSS Theorem. We are able to use this theorem because we know 3 side lengths and all we have to do is find the scale factor of one triangle, and use that scale factor to multiply with one of the side lengths of the other triangle to find the missing side length. In order to use the mirror method, you place a mirror down and then move around until you can see the object you're trying to look at in the mirror. On the left, I have my final estimation for how tall the flagpole is using the mirror method. All the numbers above are in inches not feet! The 64 represents my height, 21 represents how far I was from the mirror, and 120 represents how far the mirror was from the flagpole. I took my height and the distance from myself to the mirror to form a triangle. I then divided 64 by 21 to get the scale factor which was 3.04761905. I then took that number and multiplied it by 120 to find the missing side length which got me 365.714286".
Isosceles Triangle - Two equal angles and two congruent sides. By creating a 45 degree angle to the tip of the flag pole to the person, we can discover the height by calculating the distance from the flagpole to the person. In order to create this isosceles triangle, we used a protractor and made sure that a person was standing at a 45° from the flagpole. Once they were at that angle, we measured how far the person was from the flagpole since that would equal the height of the flagpole. The distance from the person to the flag pole is the same as the height of the flag pole since it is an isosceles triangle. When I measured the distance I got 360" and then I turned it into feet which is 30'. Therefore, for this method, I got 30 feet for how tall the flagpole is.
This problem was okay. I do have to say that I did actually enjoy this problem compared to previous ones that we've done in this class. I did struggle at some points, but I think that each method was pretty easy once I had a good understanding. The isosceles method really pushed my thinking. I think that method was the most confusing one out of all of them. For this method, I h
If I were to grade myself on this similarity unit, I would give myself a B+. The reason for this is because some of the content for similarity really confused me while a portion was easy for me to understand. Also, I didn't really push myself to try to do the work on this unit. For the similarity test we took, I got 12/18. It's not that bad but it certainly isn't good either. I think a reason as to why I didn't do that well was because my understanding of the content wasn't exactly clear. When I was asked to use a theorem and explain, I was unable to because I was confused.