Problem statement- What is the height of the flagpole? HTHCV want to create a flag for their school so they can raise it on the flagpole. They then realize that there are certain flag requirements based on the height of the flagpole. For this problem we need to figure out the height of the flagpole by using different methods of math.
Process & Solution
When we were first given this problem each student had to make a guess on how tall the flagpole is. We all went outside to look at the flagpole and people were standing next to the pole to see how much bigger it is than them we then went back inside and had a discussion with our table group about how tall it is. My guess was that 25 feet was the minimum with 33 feet as the max height. Something that we were told that we were going to see a lot during this problem was Similarity. Similarity is can be explained in four words, "Same Shape, Different Size" meaning that the angles will be the same for both shapes but it can be a different size from the original.
First method- Shadow method The first method that we were introduced to was the shadow method. we were given a worksheet to understand what this method does and how to do it. First we wrote a proportion to find the height. This method works because of the Angle Angle theorum,we are given a right triangle of 90 degrees and an anle that is given to us by the sun, a 45 degree angle.
My height = Flagpole height My shadow Flag pole shadow
This helped us figure out what measurements we needed to use in order to calculate the height of the flagpole. Then with our groups we went outside to measure our heights and our shadows, after we wrote down those measurements we used our tape measure to see how long the flagpoles shadow was. The flagpole's shadow was 408 inches.
Nick - 69 in = x Anthony- 71 in = x Ana- 63 in = x Me- 63 in = x 116 in 480 in 116 in 480 in 100 in 480 in 100 in 480 in
Since Ana and I's were the exact same we decided to use that proportion and we solved it. we divided 100 by 63 and got 1.58 as our answer. then we put 1.58 where x was and divided 480 by 1.58 and got 303 in , then to convert it into feet we divided 303 in by 12 and got our final answer, 25.25 ft.
Second method- the mirror method The second method that our teacher presented us with was the mirror method. with this method you take a mirror, place it on the ground and try to position yourself as close or as far as possible until you can find the top of the object your trying to calculate. the reason why this works is because the two triangles are similar, showing us the angle angle similarity theorem. if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
our teacher taught us how to do this by showing us an example. he placed the mirror on the ground and said he wanted to find the height of the projector he went back and forth until he found the top of the projector. and to find the measurements he would have to know the distance between him and the mirror, his height, and the distance between the object and the mirror. then it was time for the class to try out this method. Each group was given an mirror and a tape measure. We had to give variables for the measurements.
Persons height- p horizontal distance from person to mirror- D horizontal distance from mirror to object-Y object height-X
My group then made an equation out of the variables we had just made Y = X horizontal distance from mirror to object = objects height D P horizontal distance from person to mirror persons height
We used this method of other things before we did the flagpoles height. for example we did the basketball hoop. we got 53 = x after getting these numbers we crossed multiplied to get X. we then got 123.6 inches 27 63
after finding multiple objects height we finally did the flagpoles height
217 = x We then crossed multiplied this and got 379.7 = X to convert this into feet we divided by 12 and our 36 63 finalanswer was 31.7 ft
Third method - clinometer method the first thing that we had to know before using this method was know what an isosceles triangle was. An isosceles triangle is a triangle with two angles that have two sides of the equal length.
A clinometer is a tool that is used to measure the angle of a tall objet in a right angled triangle. It works because the Clinometer has a paper clip hanging from the flat side of a protractor and when you want to find the distance between you and the object you have to make sure that the paper clip is at a 45 degree angle.
this is what our group calculated, we had Ana use the clinometer because she had the average height of the group. after getting our final answer, 375 inches, we divided it by 12 to convert it into feet and our final answer was 31.25 ft. this method works because its an isosceles triangle so the base is the same height.
Best Final Estimation I think that my final estimation for the height of the flagpole is 31 feet because our shadow method height was 25.25 ft, our mirror method was 31.7 ft and our clinometer was 31.25ft. and with the clinometer method it has a fixed angle of 90 degrees and another 45 degrees, making it the AA theorem.
Problem Evaluation
I enjoyed this problem because we were able to learn about similarity, and about different triangles and the different theorems and why they work. I also enjoyed with how much we were involved with our table groups by going around the school to take measurements and then going back into the classroom to do the calculations. Along with that, learning about the different methods that will help you find the height of something, shadow method, mirror method and the clinometer method.
Self Evaluation
If I were to grade myself I think I would give myself an A because of how much I've contributed to the group with sharing my ideas and helping my group members if they've made a mistake. Also because during the similarity test revisions I was able to help other people with problems that they needed help with.
Edit Section- critiques I got from my peers
Title "Height of the flagpole" I made this change
Capitalize "Edit Section" I made this change
Capitalize "Best Final Estimation" I made this change
Space out the sections I made edits to the page by spreading out the writing and pictures from each other
Add more to the problem statement ( the part in bold is what i added)
HTHCV want to create a flag for their school so they can raise it on the flagpole. They then realize that there are certain flag requirements based on the height of the flagpole. For this problem we need to figure out the height of the flagpole by using different methods of math. For this problem we need to figure out the height of the flagpole by using a variety of different methods. Before we used The shadow method, the mirror method and the clinometer method, We had to Learn what Similarity is and how it will help us with the different types of methods