# Math Help - Long’s Peak

1. ## Long’s Peak

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

a. Solve this equation for h.

I got (D^2)/1.44) = h

Is that correct?

b. Long’s Peak in the 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)?

This is my set up:

D = 1.2(sqrt{14,255})

Do I solve for D and then compare my answer to 89 miles?

2. Originally Posted by magentarita
The equation D = 1.2(sqrt{h}) gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.

a. Solve this equation for h.

I got (D^2)/1.44) = h

Is that correct?

b. Long’s Peak in the 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)?

This is my set up:

D = 1.2(sqrt{14,255})

Do I solve for D and then compare my answer to 89 miles?

a) Yes, first one is right.

$D = 1.2\sqrt{h}$

$\Rightarrow h = \frac{D^2}{1.44}$

b) $D = 1.2\sqrt{h}$

$D = 1.2\sqrt{14,255}$

D = 143.27 feet

Now convert this into miles. If it comes out to be greater than 89 miles, then the person can see Cheyenne, Wyoming, otherwise not.

3. ## how..

Originally Posted by Shyam
a) Yes, first one is right.

$D = 1.2\sqrt{h}$

$\Rightarrow h = \frac{D^2}{1.44}$

b) $D = 1.2\sqrt{h}$

$D = 1.2\sqrt{14,255}$

D = 143.27 feet

Now convert this into miles. If it comes out to be greater than 89 miles, then the person can see Cheyenne, Wyoming, otherwise not.
How do I convert 143.27 feet to miles?

4. Originally Posted by magentarita
How do I convert 143.27 feet to miles?
You don't. The original problem said "The equation D = 1.2(sqrt{h}) gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet." Shyam mis-spoke when he said it was 142.26 feet.

5. ## ok...

Originally Posted by HallsofIvy

You don't. The original problem said "The equation D = 1.2(sqrt{h}) gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet." Shyam mis-spoke when he said it was 142.26 feet.