To find out how much farther Addison can see to the horizon compared to Kaylib, we can follow these steps:
1. Given Heights:
- Kaylib's eye-level height is [tex]\( 48 \)[/tex] feet.
- Addison's eye-level height is [tex]\( 85 \frac{1}{3} \)[/tex] feet, which can be written as [tex]\( 85 + \frac{1}{3} \)[/tex] feet or [tex]\( \frac{256}{3} \)[/tex] feet.
2. Distance to the Horizon Formula:
The formula to calculate the distance to the horizon [tex]\( d \)[/tex] (in miles) based on the eye-level height [tex]\( h \)[/tex] (in feet) is:
[tex]\[
d = \sqrt{\frac{3h}{2}}
\][/tex]
3. Calculate the Distance for Kaylib:
Using Kaylib's height ([tex]\( h = 48 \)[/tex]):
[tex]\[
d_{\text{Kaylib}} = \sqrt{\frac{3 \times 48}{2}} = \sqrt{\frac{144}{2}} = \sqrt{72}
\approx 8.48528137423857 \, \text{miles}
\][/tex]
4. Calculate the Distance for Addison:
Using Addison's height ([tex]\( h = 85 \frac{1}{3} \)[/tex]):
[tex]\[
d_{\text{Addison}} = \sqrt{\frac{3 \times 85.333333}{2}} = \sqrt{\frac{256}{2}} = \sqrt{128}
\approx 11.313708498984761 \, \text{miles}
\][/tex]
5. Calculate the Difference in Distance:
To find how much farther Addison can see compared to Kaylib:
[tex]\[
d_{\text{difference}} = d_{\text{Addison}} - d_{\text{Kaylib}} \approx 11.313708498984761 - 8.48528137423857
\approx 2.8284271247461916 \, \text{miles}
\][/tex]
Hence, Addison can see approximately [tex]\( 2.8284271247461916 \)[/tex] miles farther than Kaylib to the horizon. This value simplifies to [tex]\( 2\sqrt{2} \)[/tex] miles, which matches one of the answer choices.
Therefore, the correct answer is:
[tex]\[ 2\sqrt{2} \text{ miles} \][/tex]
