Find the distance to the horizon @ 32,000 feet.

assuming you mean on the earth, not some other planet or polyhedral body,

If d is the distance, and r is the radius of the earth (in feet),

r^2 + d^2 = (r+32000)^2

If d is the distance, and r is the radius of the earth (in feet),

r^2 + d^2 = (r+32000)^2

To find the distance to the horizon at a certain height, we can use the formula for the distance to the horizon which is given by:

Distance to Horizon (in nautical miles) = 1.2247 * sqrt(Height (in feet))

Let's calculate the distance to the horizon at a height of 32,000 feet using this formula:

Distance to Horizon = 1.2247 * sqrt(32,000)

First, let's calculate the square root of 32,000:

sqrt(32,000) = 178.8854

Now, let's calculate the distance to the horizon:

Distance to Horizon = 1.2247 * 178.8854 = 218.7153 nautical miles

Therefore, the distance to the horizon at a height of 32,000 feet is approximately 218.72 nautical miles.