Question

City A and city B are approximately a=350 miles apart on the surface of the earth. Assuming that the radius of the earth is 4000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has city A on one side and city B on the other side.

Answer 1

Use the formula S=rθ. 
θ=radian measure of the central angle.   r=radius.  S=central arc=a=350. 

so...
350=4000θ  
350/4000=θ
0.0875=θ
 
so 0.0875 radians is the central angle.