Indirect measurement project
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Siddharth and Ryan used indirect measurement and similar triangles to calculate the height of a soccer net. They measured their own heights and shadow lengths, as well as the shadow length of the net. By setting up proportions between the triangles formed, they were able to calculate the height of the net, which they determined to be approximately 270.9 cm. Their measurement may not be exact due to changes in shadow lengths throughout the day as the sun's position changes.
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Indirect measurement project
- 2. ï‚¡ Our goal was to find out the height of the soccer net. ï‚¡ We did this by using indirect measurement.
- 3.  Height of: oRyan: 174 cm oSiddharth: 158 cm  Length of: oRyan’s Shadow: 100 cm oSiddharth’s Shadow: 90 cm  Length of Soccer Net’s Shadow: 155 cm
- 4. This is a picture of the scenario: Height (Ryan: 174 cm) Siddharth: 158 cm (Side of soccer net) Shadow (155 cm) Shadow (Ryan: 174 cm Siddharth: 158 cm)
- 5. ï‚¡ Similar: Corresponding angles are equal in measure ï‚¡ The triangles that were formed in the last slide are similar
- 6. ï‚¡ Triangles are similar because their corresponding angles are equal in measure ï‚¡ We know this because: oThere is a right angle, which we know is 90 degrees oAlso, since the light was coming at the same angle for both us and the soccer net, the top angles must be equal in measure. oSo, if two angles in two triangles are equal to each other, then the third angles must also be equal oTherefore, the triangles are similar
- 7.  Since we knew that the triangles were similar, we could set up a proportion: oWe did it for both of our heights. Using Ryan’s height: Using Siddharth’s height:
- 8. ï‚¡ We got different answers for each of us, so we found the average between the two answers ï‚¡ We got 270.9 cm as our answer ï‚¡ So, the height of the soccer net is approximately 270.9 cm.
- 9. ï‚¡ We may not be 100 percent exact on the measurements ï‚¡ The length of the shadow changes throughout the day because it depends on where the sun is in the sky. oSo if we had taken the measurements later or earlier in the day, the lengths of the shadows may have been different.