Problem Statement
In this problem we had to figure out the height of the flagpole because no one on campus knows what it is and we wanted to get a flag but there are regulations for how big it is depending on the height of the flagpole. To do this we used a lot of methods that you will learn about in the process and solution.
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Process an solution
My initial guess was that it would be around 30 ft. I was pretty close in all three methods we were pretty close to the same heights as we were going. To do this problem we had to understand similarity and there was a couple ways for us to figure out how they were similar. Similarity is when they are the same shape but it could be either bigger or smaller. The ways that you can prove that shapes are similar are if they have the same angles and the side lengths are proportional.
Shadow Method
For the shadow method We had to calculate the height of the flagpole using the shadow of the flagpole and our height and our shadows. To do this we had to figure out the scale factor and to do that we would just divide the 2 numbers and find out the scale factor. Once we got the number we multiplied it by the height of the person and thats how we got the height of the flagpole. This was pretty simple because you would set up the proportion because you knew that the triangles were similar because of the way that you were standing next to the flagpole and the way that the sun was hitting it would give the same angle creating AA similarity.
for this method we got 29.14ft
Shadow Method
For the shadow method We had to calculate the height of the flagpole using the shadow of the flagpole and our height and our shadows. To do this we had to figure out the scale factor and to do that we would just divide the 2 numbers and find out the scale factor. Once we got the number we multiplied it by the height of the person and thats how we got the height of the flagpole. This was pretty simple because you would set up the proportion because you knew that the triangles were similar because of the way that you were standing next to the flagpole and the way that the sun was hitting it would give the same angle creating AA similarity.
for this method we got 29.14ft
Mirror Problem
For the mirror method you had to place the mirror in the middle of you and the flagpole and you had to be able to see the top of the flagpole from where you were standing. My group and I did that wrong so we had to go measure it again. To figure out the height of something using this method you have to measure your height the length from you to the mirror and the length of the flagpole to the mirror. Then you would divide your your distance to the mirror by the distance to the the flagpole from the mirror and multiply that by your height and that would be the height in inches so you would divide by 12 if you want it to put it into feet. For this method the theorem that I used was the AA Theorem because they have 2 equal angles in them the right angle and then the one coming from the mirror.
For this method we got 40ft |
Clinometer Method
Problem evaluationI really enjoyed this problem because I felt that I had learned a lot of different ways not only for similarity but for other problem solving things because of the way we had to learn how to set everything up and to do other things to solve for a certain thing. I really think that this problem was real and that made us more excited to figure it out instead of trying to figure out something that already has an answer, it was more exciting.
Edits
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For the clinometer method we had a protractor that had a straw along the bottom and a string tied to the little hole with a paper clip at the bottom serving as a weight. You would look through the straw and find the top of the flagpole but the angle had to be 45 degrees because we knew that it was an isosceles triangle. Once you found that you would measure the length of you to the flagpole and the height until your eyes. Once you had both of those lengths you would add them together and that was the height of the flagpole. The theorem that we used was angle angle because it was an isosceles triangle so we had to find the 45 degree angle and that caused us to back up until we found it and it made angle angle.
For this Method we got 32 ft My final estimation for the flagpole is 30ft. I think that it is about 30ft because that is super close to the average of the flagpole and I believe that they wouldn't put a random number with lots of decimals as the height. Self evaluationI think that for this problem I deserve an A because I was working every time we had something to do and I just really enjoyed the problem and it made it easier to focus because I genuinely enjoyed the problem. Every day I came in ready to do math and I would expect my group mates to be the same and even if they didn't understand it I would try to explain it to them. I feel like I was excited to do work and tried my best to understand what we were doing, I think I did a pretty good job.
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