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Answer: 1589.65 miles</h3>
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Explanation:
The degree of separation from the two cities is 30-7 = 23 degrees.
Let's say the point C is at the center of the earth. This would mean angle BCA is 23 degrees.
Any longitude line helps form what is known as a great circle or orthodrome. This is a math term that describes a circle that is centered at the same location as the sphere's center. Imagine that you can wrap a string around the earth and this string only follows this particular longitude line. This string is effectively a vertical equator in a way. The question is: what is the length of this string?
Well that would be the circumference of the circle with radius 3960 miles because the longitudinal circle has the same radius as the sphere.
That approximates to...
C = 2*pi*r
C = 2*pi*3960
C = 24,881.4138164311
C = 24,881.41
So a bit less than 25 thousand miles. I used the calculator's stored version of pi rather than something like 3.14 to get the best accuracy possible. This is the full string's length if we want to travel the entire distance around the globe but stay entirely on this particular longitude line
We don't want the full string's length. Instead, we want just a fractional portion of it. Specifically, we want 23/360 of it because of the central angle of 23 degrees. This will give us the distance between the two cities.
So (23/360)*24,881.4138164311 = 1,589.64588271642
This then rounds to 1589.65 when rounding to the nearest hundredth.
The distance between the two cities is approximately 1589.65 miles
This is comparable to the driving distance from Los Angeles, CA to Houston, TX (approximately 1547 miles).
