Introduction
Everyday I would drive past the flag pole on the right side of the school but it has never occurred to me to calculate the actual height. Using the Shadow Method, Mirror Method, and Isosceles Method we concluded a mind pushing final estimation of the HTHCV flagpole.
Process & Solution
What do you think is the height of the flag pole below?
My initial guess: Minimum was 30 ft.- Maximum was 80 ft.
Why? My guess was pretty unreasonable and ridicules but this was my guess. My reasoning was "I felt it wouldn't be any bigger than 100 ft. from past observations" I honestly tried to come up with a logical reason why.
Then, we went outside to see the actual flag pole. I had to think of ways I can make a more accurate prediction of the height. It definitely looked taller than I remembered from this morning.
My new prediction: Minimum was 80 ft.- Maximum was 150 ft.
Why? My guess was pretty unreasonable and ridicules but this was my guess. My reasoning was "I felt it wouldn't be any bigger than 100 ft. from past observations" I honestly tried to come up with a logical reason why.
Then, we went outside to see the actual flag pole. I had to think of ways I can make a more accurate prediction of the height. It definitely looked taller than I remembered from this morning.
My new prediction: Minimum was 80 ft.- Maximum was 150 ft.
Before learning about the flagpole problem, we learned about similarity.
Shadow Method
How to measure a tall object with the sun. How cool is that?
This method is the Side, Side, Side Theorem. We are using three corresponding sides and comparing ratios to see if these are similar.
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Here we are going to compare two shadows by ratios. By using the sun we measured a person's shadow height and the flagpoles shadow height. We measure the exact height of the person then compared it by using ratios. x : Shadow of the flagpole to
Height of the person : person's Shadow height this will get you the scale factor (how many times bigger each object is from each other) and solve for x. The sun cast the same angle on both objects, like a similar triangle! |
How we applied the Shadow Method to our own flagpole...
We went outside, measured our height in the classroom.
My partners were the same height: 5'4 ft.
I was: 5'5 ft.
But we decided to go with their height.
We measured our shadow theirs was: 8 ft.
Mine was: 8'1 ft.
But we went for their shadow instead
Then, we measured the flagpoles shadow and boy was it a long shadow
Flagpoles shadow: 55 ft.
Flagpoles unknown height was x
My partners were the same height: 5'4 ft.
I was: 5'5 ft.
But we decided to go with their height.
We measured our shadow theirs was: 8 ft.
Mine was: 8'1 ft.
But we went for their shadow instead
Then, we measured the flagpoles shadow and boy was it a long shadow
Flagpoles shadow: 55 ft.
Flagpoles unknown height was x
Knowing this information, we compared the ratios and solved it mathematically.
5.4/8=.675
.675 x 55= 37.125
My estimated solution is that the flagpole is 37.125 ft. tall.
5.4/8=.675
.675 x 55= 37.125
My estimated solution is that the flagpole is 37.125 ft. tall.
Mirror Method
The person is moving towards or farther away from the mirror until you can see the object making two triangles. One of the unknown height of a tall object like a flagpole and one of a known height of a person.
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Using these possibly similar triangles we will see if the sides correspond and the angles appear to be the same.
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Using a mirror we measured our height, the length between the mirror to the person, the length between the mirror to the object, and we had to make sure that we can see the top of the object through the mirror on the ground. By comparing ratios of the three known lengths.
Our calculations of the mirror method to the flagpole:
-64 in. or 5.33 ft. is the height of the person
-21 in. or 1.75 ft. measurement of distance to the person to the mirror
-120 in. or 10 ft. is the distance from the mirror to the object
We divided 5.33 ft by 1.75 ft.= 3.05 ft.
10 ft. x 3.04 ft. =30.4 ft.
My estimate is 30.4 ft.
Our calculations of the mirror method to the flagpole:
-64 in. or 5.33 ft. is the height of the person
-21 in. or 1.75 ft. measurement of distance to the person to the mirror
-120 in. or 10 ft. is the distance from the mirror to the object
We divided 5.33 ft by 1.75 ft.= 3.05 ft.
10 ft. x 3.04 ft. =30.4 ft.
My estimate is 30.4 ft.
Clinometer Method
Isosceles Triangle
Problem Evaluation & Self Evaluation
Did I enjoy this problem? I didn't because I felt as though I had no direction. I was sent out to understand a concept I haven't even learned yet even after being introduced to it, I studied it on my own time but the class confused me more. I work well with rules and what I can or cannot do. I struggled minorly but even small mistakes can affect your whole solution and it has me frustrated. It was so many theorems and project hands on learning I lost track of what I have to do when I come across a problem on a textbook or a test. I was kind of just...floating into the unknown and not prepared to face another obstacle. For example, I got a 11/18 on my test. Most of them minor mistakes and some I didn't even know where to begin.
If I were to grade myself I would give myself a B. I feel as though I don't deserve an A because I lacked interest and determination to understand a problem. If I were to be asked a question on a problem by a student I wouldn't be able to answer halfway. I am really disappointed in myself though I helped others when I was able to.
If I were to grade myself I would give myself a B. I feel as though I don't deserve an A because I lacked interest and determination to understand a problem. If I were to be asked a question on a problem by a student I wouldn't be able to answer halfway. I am really disappointed in myself though I helped others when I was able to.