If you are looking at the horizon, you can determine the distance you are from the horizon in miles, D, from a height, h, in feet by the equation of D = . If you are standing on a mountain top that is 12,000 feet in elevation, how far are you from the horizon?

You did not state the equation that you should use.

Since you are not using metric units, I would have to look up the non-metric formula.
I will let you do that.

To determine the distance you are from the horizon using the given formula, we need to plug in the values of the height (h) and solve for the distance (D).

Given:
Height (h) = 12,000 feet

The equation for determining the distance to the horizon is:
D = √(2Rh + h²)

To solve the equation, we need the value of the Earth's radius (R). The average radius of the Earth is approximately 3,959 miles or 20,902,000 feet.

Plugging in the values:
D = √(2 * 20,902,000 * 12,000 + 12,000²)

Now we can calculate the distance (D) by performing the necessary calculations:

D = √(502,080,000,000 + 144,000,000)
D = √(502,224,000,000)
D ≈ 22,415,053.75 feet

To convert this distance from feet to miles, we divide by the conversion factor of 5,280 feet per mile:

D ≈ 22,415,053.75 / 5,280 ≈ 4,243.61 miles

Therefore, if you are standing on a mountain top that is 12,000 feet in elevation, you are approximately 4,243.61 miles away from the horizon.