Problem Statement
In this problem we were asked to find the length of the schools flagpole. Of course, the flagpole is way too tall to measure with a measuring tape, so we had to use alternative methods including: the shadow method, the mirror method and the clinometer method.
Process and solution
When we first started this problem we were asked what our guest of the flagpoles height would be. The way I first looked at it was “how many me’s stacked up will equal the flagpole” Since I am about 5 foot two I imagined, about 4 to 6 me’s stacked up to reach the flagpole height. I ended up rounding it down to around 20 to 30 feet tall for my estimated height.
What similarity is, is when there are two shapes, that are the exact same shape but in different sizes. Generally for a set of shapes to be somewhere the English should be equal and the sides should be proportionate
The Shadow Method
One of the methods we used to estimate the height of the flagpole was the shadow method. How we did it was we compare our height and our shadows height to the flagpole and the flagpole shadows height. This forms two similar triangles because you and your shadow create one triangle and the the flagpole and its shadow create the other one.
What we did to find the height using this method was we measured one of our table mates height and them we measured the length of the of their shadow. After that we measured the length of the flagpoles shadow and that left the height of the flagpole as x. We set up proportion and then cross multiplied to find the final height.
The Mirror Method
We also used the mirror method to estimate the height of the flag pole was the mirror method were we placed a mirror on the floor at a point were we could see the object in the mirror, since we already knew the height of ourselves what we measured to find the length of the flag pole was the base of the flagpole to the mirror , and the mirror to our feet leaving the height of the flagpole at x. Then we cross multiplied to find out what x was.
The Clinometer Method
For this method we used a clinometer, which is a straw and a string attached to a protractor, to help us find the length of the flagpole. A clinometer is a tool that is made to measure the angle of elevation, in a triangle with a right angle. In this case the triangle would be an isosceles triangle, which is a triangle that has two sides of equal length. Usually you would use a clinometer to measure really tall objects you couldn't reach with a measuring tape, so it would be perfect for the flagpole height.
To use a clinometer for this method, you have to look through the hole of the straw and move forward and backward with until the string lands on the 45 degree angle. Then you have to measure the horizontal distance from the base of the object to your feet and then the vertical height from your feet your eyes. Then you would add the vertical and the horizontal heights.
Final Estimation
My best final estimation for the height of the HTHCV flagpole would be 25.9, to find this number I found the average (add all numbers together, then divide by the amount of numbers there are.) I thought this would be a good way to determine the best flagpole height estimate because it gives you the exact middle.
Problem Evaluation
This problem was actually a lot of fun in my opinion. I feel I was able to learn a lot because while testing out methods we were able to go outside and actually see how the method works.
Self Evaluation
I really do feel like I deserve an A+ since I worked really hard to be able to understand the topic. Whenever it got tough I would ask questions and work through the problem with my table mates.