Problem Statement:
Mr.Tim wants to get a new flag for HTHCV flagpole but there is a regulation of the flag size based on the flagpole's height so in order to know what its the size of the ideal flag we need to know the size of the flagpole to get our new HTHCV flag.
Below there are some estimations of different methods we have tried so far to solve this problem and our justification of them. |
Process and Solution:
Initial Guess:For my initial guess I said the flagpole was 9 meters but I had to convert them to feet scince everyone else's guess was on feet so I searched up how to convert meters to feet and I had to multiply 3.280 by 9 and I got 29.52ft.
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What is similarity?Similarity in my own words is figures that have same shape and that have their corresponding sides are proportipnal , also they must have equal angles
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Shadow Method:
At the beginning of this method we had to figure out what woukd the equation be so with the diagram showing here we cocluded that this is what the equation will look like: (my shadow/my height = flagpole shadow/flagpole height).
We know the triangles are similar because the theorem of Angle Angle cause as we can see in the image both of them share a 90 degree angle and also both ofthem will share the angle of the top because the sun makes both objects have the shadow that goes down in the same position so they share the angle from the top to the floor. To solve this problem using this methos my team and I divided our heights by our shadow and got how may times our shadow was bigger than our normal height and we got an average of 2.13 times so we multiplied that by 10ft 45in and got that the flagpole estimated height was 29.39 ft. |
Mirror method
We know the mirro method uses the Angle Angle theorem because they share a 90 degree andgle and both objects are staring to the same mirros so it creates the same angle.
using the mirror method we had to know the 3 imputs involved in order to solve the problem so our imput #1 was 64in, #2 6 in, #3 21in, we has to corss multiply and divide and we got a aproximate heigt of the flagpole was 18ft. |
Clinometer Method
We know the triagles we use to campare are similar because we use the thorem of Angle Angle because we know that both triangles share a 90 degree and since the clinometer is pointing (looking) at the same part they share the angle from the top.
In order to have an estimation of the flagpole's height me and mi team got the measurements of the horizotal distance from me to the baste that was 314 in, then vertical distance from the to the gorund that was 62 in and add those to then divide them byh 12 and make then in feet, Our estimation was 31.33 ft. |
Final estimationMy estimated height wil be 31.33 because the clinometer for me it makes more sense the process based in what we did and seems more reliable.
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Problem evaluationI really liked the problem cause because it involves so much things we have been learnign throughout the year but at the same time learning new things like more about a new geometry side we didn't knew about.
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Self evaluation
I really liked this problem because we over pased thing we've learned before but now more more difficult and this problm made us figure out noew ways to salve the problem as mking us se how geometry works with the methods we have learned to prove similarity.