Question

You are in a hot air balloon, 650 m above the flat Texas plains. The Earth's radius is about 6400 km.You look out toward the horizon. How far out can you see−that is, how far is your horizon?

Answer 1

91 km

Step-by-step explanation:

Draw a picture. The line of sight to the horizon forms a tangent line with the curvature of the Earth. The radius line to that point forms a right angle with the tangent line. So we can use Pythagorean theorem to find the distance.

c² = a² + b²

(6400 km + 0.650 km)² = (6400 km)² + d²

d ≈ 91 km