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. 

Answer 2

The radian measure of the given central angle in the question is; θ = 0.0875

How to find the Central Angle?

The formula for central angle here is;

θ =  Arc Length/Radius

We are given;

Arc length = 350 miles

Radius = 4000 miles

Thus;

θ = 350/4000

Radian measure of central angle is; θ = 0.0875

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