My original guess for the height of the HTHCV flagpole was: 30-70 ft
My final estimate for the height of the HTHCV flagpole is: 68.75ft
In the flagpole problem we had to figure out the height of our school's flag without actually measuring it. When we first got introduced to the problem we had to guess the height of the flagpole and mine was
Min: 30 ft. Max: 70ft
After we took our first initial guess we went outside to take a look at the flag to see ways we could figure out the height. Then we took a second initial guess after seeing the flagpole at mine changed a little bit
Min: 40 ft. Max: 90 ft.
As a table we came up with ideas on how to solve this problem and some ideas we had were a bit silly like
- Photoshop Alejandro and place him on top of himself multiple times so we could figure it out.
But we came up with other reasonable ones like,
-Just call the company that makes them to figure it out
-Get mobile elevating work platforms and try to measure it from the top
There were plenty of other ideas. While trying to figure all this out we had to explain the mathematical definition of similarity my explanation was very straight forward. "Objects that are similar to each other, but not quite" The actual definition of similarity is
"Geometry. (of figures) having the same shape; having corresponding sides proportional and corresponding angles equal: similar triangles." (Google)
So in the end I was somewhat on the right track
My final estimate for the height of the HTHCV flagpole is: 68.75ft
In the flagpole problem we had to figure out the height of our school's flag without actually measuring it. When we first got introduced to the problem we had to guess the height of the flagpole and mine was
Min: 30 ft. Max: 70ft
After we took our first initial guess we went outside to take a look at the flag to see ways we could figure out the height. Then we took a second initial guess after seeing the flagpole at mine changed a little bit
Min: 40 ft. Max: 90 ft.
As a table we came up with ideas on how to solve this problem and some ideas we had were a bit silly like
- Photoshop Alejandro and place him on top of himself multiple times so we could figure it out.
But we came up with other reasonable ones like,
-Just call the company that makes them to figure it out
-Get mobile elevating work platforms and try to measure it from the top
There were plenty of other ideas. While trying to figure all this out we had to explain the mathematical definition of similarity my explanation was very straight forward. "Objects that are similar to each other, but not quite" The actual definition of similarity is
"Geometry. (of figures) having the same shape; having corresponding sides proportional and corresponding angles equal: similar triangles." (Google)
So in the end I was somewhat on the right track
Shadow Method
In the shadow method we first measured ourselves and then went outside to measure our shadow. This gave us an idea for the shadow method. So then we measured the shadow of the flagpole and tried to find the value of X which was the flagpole in this case. With the given information of our heights and shadow it helped guide us a little bit.
Mirror Method
Another method we used was the mirror method. For this method we first tested out with different objects around the school. In order to do this we first had to measure the height of one of our table mates. Then we were given a mirror and we had to place it one the floor in front of the object we wanted to measure for example we wanted to figurre out the height of the light fixures in the hallway. So our first step was to place the mirror on the floor and the one tablemate that was measure had to find the light fixure through the center of the mirror we then measure the distance from their feet to the mirror and the distance from the mirror to the object. We did this for several other objects after we did it to every object we then did the calculations to figure it out
Light Fixure in hallway
Input #1 (height of person) : 59"
Input #2 () : 31"
Input #3 () : 67"
59 . 67 / 31 . x ----- 59.67 = 3,953 Then 31.x becomes 31x and you try to get 31 by itself so it becomes 31x/x
and what you do to one side you have to do to the other so 3,953/31 = 127.51
We did to all the objects and found the output for each one of them.
Another method we used was the mirror method. For this method we first tested out with different objects around the school. In order to do this we first had to measure the height of one of our table mates. Then we were given a mirror and we had to place it one the floor in front of the object we wanted to measure for example we wanted to figurre out the height of the light fixures in the hallway. So our first step was to place the mirror on the floor and the one tablemate that was measure had to find the light fixure through the center of the mirror we then measure the distance from their feet to the mirror and the distance from the mirror to the object. We did this for several other objects after we did it to every object we then did the calculations to figure it out
Light Fixure in hallway
Input #1 (height of person) : 59"
Input #2 () : 31"
Input #3 () : 67"
59 . 67 / 31 . x ----- 59.67 = 3,953 Then 31.x becomes 31x and you try to get 31 by itself so it becomes 31x/x
and what you do to one side you have to do to the other so 3,953/31 = 127.51
We did to all the objects and found the output for each one of them.
Isosceles Method
"In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case." (Google)
Lastly we were introduced to this last method. When we were given this method we were asked to discuss what we know about an isosceles triangle and I wrote that its 2 sides and angles that are the same. The way of figuring it out through this method was by looking at the flag pole like an isosceles triangle.
"In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having two and only two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case." (Google)
Lastly we were introduced to this last method. When we were given this method we were asked to discuss what we know about an isosceles triangle and I wrote that its 2 sides and angles that are the same. The way of figuring it out through this method was by looking at the flag pole like an isosceles triangle.
In order to figure this out we had to use a protractor. So we went outside and we had someone point at the flagpole we then used the protractor and linked it up with the flagpole and person. We tried to do it at 45 degrees. We spent 30 minutes trying to figure out we went from spot to spot because we couldn't get the measurement right. Then after we finally got it.
Average guess : 68.75
Shadow method : 37.5
Isosceles method : 24
These were our final estimates for each method. These seems to be the most accurate because we did the calculations as a table and we all rounded up with the same answers.
Shadow method : 37.5
Isosceles method : 24
These were our final estimates for each method. These seems to be the most accurate because we did the calculations as a table and we all rounded up with the same answers.
Problem Evaluation-
The flagpole problem was definitely a challenging problem I had to come across some methods that I had never tried before. I really pushed myself by trying new things and I was dedicated to trying to figure the answer so I pushed myself even more. Overall I feel as if this problem was the most difficult for me to figure out because so many things were involved.
Self Evaluation-
If I were to grade myself I would give myself an B because I really pushed my thinking and this time I wasn't afraid to ask my classmates for help when I was stuck on figuring things out. I rarely go off task because I was determined.
Edits-