## Problem Statement

High Tech High Chula Vista is in need of a new flagpole to be able to replace the old one. But there's one problem they can't figure out and that is what is the height of the flagpole. They need to know how tall it is in order to replace it. We had to find multiple ways to solve for the height of the flagpole.

## Process & Solution

When we first started this problem we had to make an initial guess of the flagpole was 25 ft. What I used to make this guess was the basketball court they seemed around the same length when picturing it.

What is similarity? Similarity is when you have two polygons that are the same but not necessarily the same size. Similarity is when you have corresponding angles that are equal, and must have the corresponding sides proportional to each other.

**Shadow Method:**

One way we used to solve for the height of the flag pole was the shadow method. We can use the shadow method two form two similar triangles because you have the flagpole and it cast a shadow straight ahead so that creates a right triangle and then we use our shadow to create another right triangle. We use theorem AA ( angle angle ) because the sun cast the shadow to the right and you it creates the same two angles at the top of the triangle, and then has two right triangles so there's one angle that's given so that's why were able to use AA theorem.

Our group set up a proportion to the diagram we had drawn which was our height, our shadows height, flagpole height which is unknown and the flagpoles shadow. After that was set up we measured one of our group members height which was 5'4 ft and the length of her shadow was 9'0 ft. Then we measured the height of the flagpoles height and we got 40 ft. Once we had our estimates we crossed multiplied to solve for the missing length of X. When we crossed multiplied and distributed and then divided our final answer for the height of the flagpole using the shadow method was 24 ft.

**Mirror Method:**

Using the mirror method we are able to create two similar triangles because it from the mirror to the person you create and then use the height of the person to create another line going up which creates a right angle and same goes for the object you drawn a line to the object and another one going up to the object. Then you drawn going to the mirror and the object and the person create two triangles that connect in the middle which creates the same angle that meets in the middle and we used AA theorem.

Our groups method was to go out and find the heights of the object and we used the mirror to find the distance. We placed the mirror on the ground and we would back or forwards to the point where you can see the object in the mirror for this case we were trying to find the height of the flagpole so we used our height in inches which was 64 inches, then the distance from the person to the mirror which varied depending on where you could see the object which we got 26 inches and the distance from the mirror to the object was 109 inches. What we did to solve for it was multiply the height of the person and the mirror to object then we divided by what we got and then we would convert our answer to ft to get the height of the flagpole. Our answer for the height was 22 ft.

Our groups method was to go out and find the heights of the object and we used the mirror to find the distance. We placed the mirror on the ground and we would back or forwards to the point where you can see the object in the mirror for this case we were trying to find the height of the flagpole so we used our height in inches which was 64 inches, then the distance from the person to the mirror which varied depending on where you could see the object which we got 26 inches and the distance from the mirror to the object was 109 inches. What we did to solve for it was multiply the height of the person and the mirror to object then we divided by what we got and then we would convert our answer to ft to get the height of the flagpole. Our answer for the height was 22 ft.

**Clinometer Method:**

Our last method we used to find the height of the flagpole was the clinometer method. Using this method you are able to create two similar triangles because you have to draw out a right angled isosceles triangle so you already have a right angle so then the triangle has to add up to 180 so the other two angles our 45 degrees since the triangle has to add up to 180, which you are able to create two similar triangles because your using the object and the person to create the triangles to find the unknown height of the triangle.

Our way of solving for the heights was to go out and measure the flagpole using our clinometer. The way it works if you have to look through the straw that's on it then you keeping moving forwards or backwards depending on if the string on the 45 degree mark and if it is that's where you measure from where your standing and the base of the object. Then measure from your eyes to the ground and with those to measurements we add them together to get the most accurate height. In our case we had 333 for the horizontal distance from you to the base then 59 for the vertical distance from your eyes to the ground and when we add them we got 392 and once converted into ft we got 32.6 ft for the height of the flagpole.

Our way of solving for the heights was to go out and measure the flagpole using our clinometer. The way it works if you have to look through the straw that's on it then you keeping moving forwards or backwards depending on if the string on the 45 degree mark and if it is that's where you measure from where your standing and the base of the object. Then measure from your eyes to the ground and with those to measurements we add them together to get the most accurate height. In our case we had 333 for the horizontal distance from you to the base then 59 for the vertical distance from your eyes to the ground and when we add them we got 392 and once converted into ft we got 32.6 ft for the height of the flagpole.

My final estimation for the height of the flagpole was 32.6 ft. I used the clinometer to get this height to get the most accurate height. This seems most accurate to me because the other measurements we took I think are to short for the height of a flagpole.

## Problem Evaluation

I liked working on this problem just because we always got the chance to outside and try new ways to measure the object with a different method each time. When first solving for X it was a little hard in the beginning but once we started finding the height of different objects it made a little easier to solve for it and we solved for the height with three different methods so it became easier.

## Self Evaluation

If I had the chance to grade myself I would give myself an A. I feel liked I really pushed my self to solve for the height and was able to work with my group to solve for X. But if I was ever lost I would ask my group members on what they had and how they got to that answer. After using three different methods I feel like I really understand how to find two similar triangles and the height of an object.

## Peer Critique

Add photos/ diagrams to the methods

Make dp more creative

Add more info to problem statement

Add more info to the mirror method problem

Edits:

I added the pictures that I was missing for each problem statement and I made some changes to the methods where I missing explanation.

Make dp more creative

Add more info to problem statement

Add more info to the mirror method problem

Edits:

I added the pictures that I was missing for each problem statement and I made some changes to the methods where I missing explanation.