Question

Micah's eye-level height is 30 ft above sea level, and Mikayla's eye level height is 120 ft above sea level. How much further can Mikayla see to the horizon?
Use the formula d=√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

Answer:

$3 \sqrt{5}$ miles.

Step-by-step explanation:

Step 1: Substitute the value 30 ft for h in the equation $d=\sqrt{\frac{3 h}{2}}$  to find the distance that Micah can see.

$\begin{aligned}d &=\sqrt{\frac{3}{9}(30)} \\&=\sqrt{\frac{90}{2}} \\&=\sqrt{\frac{90}{2}} \times \sqrt{\frac{90}{2}} \\&=\frac{90}{2}=45 \\&=3 \sqrt{5}\end{aligned}$

Step 2: Substitute the value 120 ft for h in the equation $d=\sqrt{\frac{3 h}{2}}$  to find the distance that Micah can see.

$\begin{aligned}d &=\sqrt{\frac{3(120)}{2}} \\&=\sqrt{\frac{360}{2}} \\&=\sqrt{180} \\&=\sqrt{2^{2} \times 3^{2} \times 5} \\&=6 \sqrt{5}\end{aligned}$

Step 3: Subtracting the two values, we get,

$6 \sqrt{5}-3 \sqrt{5}=3 \sqrt{5}$ miles

Thus, the distance Mikayla can see to the horizon is $3 \sqrt{5}$ miles.