## Height Of The HTHCV Flagpole Problem

**Problem Statement**

In front of High Tech High Chula Vista, we have a flagpole standing at tall height. We are learning about measurement currently and we looked at the flag pole and saw that finding the estimate of that can really test our ability of how wee been learning to measure. So we took on the task of using the three methods we learned, shadow method, isosceles triangle method, and mirror method, and saw what we can accomplish.

The questions we took on with this problem were:

The questions we took on with this problem were:

**What was your initial guess for the height of the flagpole before we took any measurements?**

What was your estimation using the shadow method?

What was your estimation using the mirror method?

What was your estimation using the isosceles triangle method?What was your estimation using the shadow method?

What was your estimation using the mirror method?

What was your estimation using the isosceles triangle method?

## Process and Solution

We started this problem by taking time out of our class time to go and examine the flagpole. When we out there, we all tried to guess what the height was just by looking at it. Then we came up with the method of let someone stand next to and compare their height to the flagpole's height. We tried to see how many of that person could fit into the flagpole's height. It was a start, but obviously it wasn't a very accurate estimate. My initial guess for the height of the flagpole was minimum 50 feet and maximum 75 feet. This whole problem though we revolved around similarity and similarity problems. When two shapes are similar is when the ratios of their lengths are corresponding to each other.

## Shadow Method

The shadow is a measuring method. You measure the lengths of two shadows, one of the shadows is a taller object that obviously can't be easy measured and the other is one object that you can easily find the height. We can use the known height of the one object to find the height of the unknown one. We can find the equivalent ratio. You can form two similar triangles for this method because you can see how the smaller triangle is similar to the larger to see if the sides are corresponding and to find the ratios and it relates to the how you look at the lengths of the shadows. Me and my partner, Thalia, worked together to first measure my height, then measure my shadow, which we then figured out how much it would take to get to the flagpole's shadow.

EXAMPLE:

My height: 5'1

Shadow length: 7ft

With my shadow's height it takes approximate five of them to reach the flagpole's shadow from one end to the other including 4 more feet.

7 x 5 = 35 + 4 = 39

And with the answer we were given we rounded it up to 40 ft.

EXAMPLE:

My height: 5'1

Shadow length: 7ft

With my shadow's height it takes approximate five of them to reach the flagpole's shadow from one end to the other including 4 more feet.

7 x 5 = 35 + 4 = 39

And with the answer we were given we rounded it up to 40 ft.

## Mirror Method

The mirror method is another measuring method. It's done setting up a mirror on the ground between you and the object you want to measure. There is also two triangles in this method because when putting the mirror on the floor, you put in front of the object and you stand in front of the mirror also, but on the opposite side of the object walking backwards or forwards until you can see the object you want to measure. At some point you will see the object. You can see it forms two triangles that you can compare the find the height. We can use the distance from the mirror to the object and the distance between yourself and the mirror and the heights of yourself and the flagpole to find the height. For our pair, we did my height,

## Isosceles Method

All isosceles triangles have two equal sides, and two equal angles. We use these because it's how we tell these triangles are similar which tells us if it's heights and ratios are correct. While calculating to decide the heights we had to make sure that they were similar and checking the two equal sides and angles is how we do that. The method we used was we took the flagpole and it's shadow and turned it into an isosceles triangle by labeling the flagpole and its shadow ABC. We out a put a person's shadow match up with the top of the flagpole's shadow. The top of the flagpole shadow is matched with the top of my shadow(which is my head). With this you get the length of you shadow and the length of the flagpole's shadow and see the ratio between you and your shadow and use the scale factor to multiply against the flagpole's shadow height.

## Problem Evaluation

I feel like this problem pushed me to think outside the box because I didn't really understand it at first until I actually asked my peers for help. It helps a lot to have people who can help you and explain the problem to you. For me, I feel like this problem helped me review triangles that I had forgotten before a long time ago.