Problem Statement
In the flagpole problem, we were asked to decipher the height of the flagpole in front of our school without measuring tapes. Through this, we learned multiple ways of solving for the height without
Process & Solution
Prior to starting any calculations, we needed to make estimates about what we thought the flagpole's height was. We would come to learn a couple methods; the shadow method, the mirror method and the isosceles method. With each of these methods, our group got different estimations compared to other groups. Throughout this unit, we learned about using similarity in shapes to distinguish a missing side of the shape. Similarity is when the two shapes you are comparing have the same scale factor. They can have different sides, but when you compare it to the other shape, when you divide the sides they will equal the same thing. We used three different theorems to figure out if two triangles were similar; SAS (side, angle, side), AA (angle, angle), and SSS (side, side, side).
In the flagpole problem, we were asked to decipher the height of the flagpole in front of our school without measuring tapes. Through this, we learned multiple ways of solving for the height without
Process & Solution
Prior to starting any calculations, we needed to make estimates about what we thought the flagpole's height was. We would come to learn a couple methods; the shadow method, the mirror method and the isosceles method. With each of these methods, our group got different estimations compared to other groups. Throughout this unit, we learned about using similarity in shapes to distinguish a missing side of the shape. Similarity is when the two shapes you are comparing have the same scale factor. They can have different sides, but when you compare it to the other shape, when you divide the sides they will equal the same thing. We used three different theorems to figure out if two triangles were similar; SAS (side, angle, side), AA (angle, angle), and SSS (side, side, side).
We can recognize that these triangles are the same because they have two similar angles. They are both right triangles, which make it have a 90 degree angle on the bottom left and the angle hitting them from the sun would also be the same.
To start, each person in the group measured themselves and the measurement of our shadow along with the shadow of the flagpole. Once we all got our own answers, we averaged them out.
Our average height for a person in our group was 62 inches and the shadow was 61 inches.
These two triangles are similar by the AA theorem because the angle ABC is equal to DEF because they are both right triangles. The other angles they share in common are BAC and FDE because the sun is hitting both from the same place.
In the mirror method, a partner needed to stand in front of the flagpole with a mirror between the flagpole and the person. The person needed to make sure that they could see the top of the flagpole when looking down at the mirror. The rest of the group measured the distance between the flagpole to the mirror and the mirror to the person looking at it. We would also measure the height of the person from their toes to their eyes. After we measured, we could figure out the height of the flagpole. We compared the distance between the pole to the mirror to the distance between the mirror to the person and equaled it to x (height of flagpole) over the height of the person. To the left, you will find out calculations and the height of the flagpole in inches. |
An Isosceles triangle has two equal sides and angles and all the interior angle must always have to add up to 180. For this method we needed to go outside, with a partner. One of us was the "pointer" and the other person is the measurer. The pointer had to stand on point C and had to point up towards the top of the flagpole. The measurer had a protractor and used it to make sure there partner was doing a 45 degree angle. Then we measured the flagpole to the pointer. My group got 460 inches, and since an isosceles triangle has two equal sides, the height of the flagpole is 460 inches or 38 feet. To get 38 feet all we did is divide 460 with 12 and rounded up.
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Problem Evaluation
I didn't really like this problem because I felt like most of it was review. Although I did learn a couple things like how there are specific methods and theorems that I could use to justify my conclusions about how I would find an answer, I would have liked to get to that part sooner. The problem itself should have taken about a week to learn the theorems and to figure out the height of the flagpole using them.
Self-evaluation
I would give myself an A because for the most part, I was on task and knew what was expected of us to learn. However, I veered off task when I was finished with the calculations and should have asked for something more to do, instead of distracting others. I think that I could have studied the theorems more to better help me on the test, but even without fully understanding the theorems, I was able to find a minor understanding that would allow me to do as best as I could throughout the unit.
Edits:
Eratzi told me to add what I needed to add in terms of content learned, so I did that.
He also said to fix a grammar mistake.