Let’s break down the problem step-by-step to find the height of the statue and the difference between the estimated and actual heights.
1. Given Information:
- The student's right arm length is 2 feet.
- The student's height is [tex]\(5 \frac{1}{3}\)[/tex] feet, which is the same as 5.3333 feet.
- The statue's right arm length is 48 feet.
- The actual height of the statue is 127 feet and 5 inches.
2. Estimating the Height of the Statue:
- First, let's find the proportionality factor. This is the ratio between the lengths of the statue's arm and the student's arm.
[tex]\[
\text{Proportionality factor} = \frac{\text{Statue's arm length}}{\text{Student's arm length}} = \frac{48}{2} = 24
\][/tex]
- Using this proportionality factor, we can estimate the height of the statue by multiplying the student's height by this factor.
[tex]\[
\text{Estimated height of the statue} = \text{Proportionality factor} \times \text{Student's height} = 24 \times 5.3333 = 128 \text{ feet}
\][/tex]
3. Actual Height of the Statue:
- The actual height of the statue is given as 127 feet 5 inches. Convert the inches to feet for easier comparison.
[tex]\[
5 \text{ inches} = \frac{5}{12} \text{ feet} \approx 0.4167 \text{ feet}
\][/tex]
- Therefore, the actual height of the statue in feet is:
[tex]\[
127 \text{ feet} + 0.4167 \text{ feet} = 127.4167 \text{ feet}
\][/tex]
4. Difference Between Estimated and Actual Heights:
- To find the difference:
[tex]\[
\text{Difference} = | \text{Estimated height} - \text{Actual height} | = | 128 - 127.4167 | \approx 0.5833 \text{ feet}
\][/tex]
Therefore:
- The estimated height of the statue is 128.0 feet.
- The actual height of the statue is 127.4167 feet.
- The difference between the estimated height and the actual height is 0.5833 feet.
Finally, rounding these results as needed:
- The estimated height of the statue is 128 feet (rounded to the nearest tenth).
- The difference between the estimated height and the actual height is approximately 0.6 feet (rounded to the nearest tenth).
