Application problems with roots

[Gr8fu13]

I think I have this figured out but I would just like to confirm it.

The equation D=1.2square root of h gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.

Solve this equation for h.

I have: Square root of h = D/1.2
h=(d/1.2)^2

The second part is: Long’s Peak in Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)? Explain your answer.

For this I have: D=1.2 * square root 14255
D= 143.273 Miles

The explaination I provided was: You can see Cheyenne because the number is greater than 89 miles in distance.

Does this sound accurate? I was worried about my explaination the most. Thanks in advance!

 

[soroban]

Hello, Gr8fu13!

\(\displaystyle \text{The equation }\\:=\:1.2\sqrt{h}\,\text{ gives the distance, }D\text{, in miles that a person can see to the horizon from a height, }h\text{, in feet.}\)
. . \(\displaystyle \text{Solve this equation for }h.\)

\(\displaystyle \text{I have: }\:h\:=\:\left(\frac{D}{1.2}\right)^2\)

Right!

Long’s Peak in Rocky Mountain National Park is 14,255 feet in elevation.
How far can you see to the horizon from the top of Long’s Peak?
Can you see Cheyenne, Wyoming (about 89 miles away)?
Explain your answer.

For this I have: .\(\displaystyle D \:=\:1.2\sqrt{14255} \:\approx\:143.273\text{ miles}\)

The explaination I provided was: You can see Cheyenne because the number is greater than 89 miles in distance.
Does this sound accurate? I was worried about my explaination the most.

I would prefer to say:
. . We can see over 143 miles from Long's Peak.
. . So we can see Cheyenne which is only 89 miles away.

 

[Deleted member 4993]

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