You are in a hot air balloon, 350 m above the flat texas plains. you look out toward the horizon. how far out can you see--that is, how far is your horizon? the earth's radius is about 6400 km.

Refer to the diagram shown below.

x =  the distance (horizon) that you can see from the balloon,

Because the radius of the earth is 6400 km, and the balloon is 350 n above the earth's surface, therefore
h = 6400 + 0.350 = 6400.35 km.

From the Pythagorean theorem, obtain
x = √(6400.35² - 6400²) = 66.934 km

Your horizon is  66.934 km (or 66,934 m)