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In this project, the objective was to determine the height of an object by using a proportion based on certain measurements. The chosen object's height was estimated by considering the height of one of the project partners, the distance of the partner from a mirror, and the distance between the mirror and the base of the object. The variable 'X' was used to represent the unknown height of the chosen object. The key goal was to convert the calculated height to feet and compare it to the actual height of the partner to assess the reasonability and realism of the estimate.
The following steps were followed to determine the height of the chosen object:
[Dannie's height: 65 inches]
To calculate the unknown height 'X,' the following proportion was used:
Proportion:
(65 inches) / (80 inches) = (X) / (30 inches)
Once the proportion was set up, X was calculated as follows:
X = (65 inches) * (30 inches) / (80 inches)
After performing the calculations, the estimated height 'X' of the chosen object was obtained.
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This value was then converted to feet for comparison with Dannie's actual height.
| Measurement | Value |
|---|---|
| Dannie's height | 65 inches |
| Dannie's distance from the mirror | 80 inches |
| Distance from the mirror to the base of the object | 30 inches |
| Calculated height of the object (X) | 24.375 inches |
| Calculated height of the object (in feet) | 2.03125 feet (approximately 2 feet) |
Based on the calculations, the estimated height of the chosen object was found to be approximately 2.03125 feet, which, when rounded, is approximately 2 feet.
| Statements | Reasons |
|---|---|
| The triangles are right triangles | Given—Mr. Visser told us that we can assume this |
| Triangles are similar | If there exists a correspondence between the vertices of two triangles such that two angles of one triangle are congruent to the corresponding angles of the other, then the triangles are similar. |
In this project, it was demonstrated that similarity in triangles can be proven even when not all angle measures and side measures are known. The estimation of ratios between Dannie's height and the chosen object's dimensions was found to be reasonably close to the actual values.
One of the intriguing aspects of this project was the flexibility to choose the objects to measure, resulting in variability among different groups' projects. This allowed for creativity and exploration in applying the concept of similarity in triangles to real-world scenarios.
Despite initial challenges in understanding how to begin the two-column proof, a solution was eventually found, emphasizing the importance of perseverance and problem-solving skills in mathematical exploration.
Project Report: Determining the Height of an Object. (2017, Jan 09). Retrieved from https://studymoose.com/document/re-similar-triangles-project
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