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Slav-nsk [51]
3 years ago
5

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 ca

n 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.

Mathematics
1 answer:
luda_lava [24]3 years ago
6 0

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.

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