The distance between two points A and B on Earth..

Question

The distance between two points A and B on Earth is measured along a circle having center C at the center of Earth and radius equal to the distance from C to the surface (see the figure). If two points A and B are 900 miles apart, express angle ACB in radians and in degrees. (The radius of Earth is approximately 4000 miles. Round your answer to the nearest minute.)
∠ACB =

∠ACB degrees and inches=

Answer 1

Use the formula:  s = rθ.

 

  s = arc length = 900 miles       r = radius = 4000 miles

 

  So, θ = (900 / 4000) radians = 9/40

 

                                             = (9/40)(180° / π) = 12.89155°

 

                                                                         = 12° + 0.89155°

 

                                                                         = 12° + 0.89155°(60' / 1°)

 

                                                                         ≈ 12°53'