Question

Wyatt’s eye-level height is 120 ft above sea level, and Shawn’s eye-level height is 270 ft above sea level. How much farther can Shawn see to the horizon? Use the formula d = square root of 3h/2, h>0 with d being the distance they can see in miles and h being their eye-level height in feet.

Answer 1

The answer is 6.7 miles further.

It is given:
$d= \sqrt{ \frac{3h}{2}}$
Wyatt’s eye-level height - h₁ = 120ft
Shawn’s eye-level height - h₂ = 270ft

The distance that Wyatt can see:
$d_1= \sqrt{ \frac{3h_1}{2}} = \sqrt{ \frac{3*120}{2 }}= \sqrt{180} =13.42miles$

The distance that Shawn can see: 
$d_2= \sqrt{ \frac{3h_2}{2}}= \sqrt{ \frac{3*270}{2} }= \sqrt{405}=20.12 miles$

The question is how much farther can Shawn see to the horizon, so we need to subtract the results:
20.12 - 13.42 = 6.7 miles