Distance between Cities Find the distance in kilometers betwee...

Question

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S

Accepted Answer

Hello, everyone. We are asked to calculate the distance between the following places. On the assumption that they were on the same North South line, we will estimate the radius of the earth to be 6400 kilometers and express the final answer to the nearest kilometer. The places we are given are Nang Vietnam at 12 degrees north and Ha Fong Vietnam at 21 degrees north. Our answer choices are a 1005 kilometers B 320 kilometers C 3686 kilometers, D 1173 kilometers. So to begin with, I am going to think about what formula to use and I'm gonna use the one that finds me the arc length. So we're gonna say s is arc length and that equals the radius multiplied by the central angle. So the arc length is gonna be our distance between these two places. So that's what we're looking for. We were told our radius it is approximately 6400 kilometers. We do need to find our central angle theta we can do this by subtracting the absolute value of our two locations. So we have 21 degrees and 12 degrees. The absolute value of this will be nine degrees. However, to use this formula, we don't want our central angle to be in degrees. We want it to be in radiance. So we're gonna take nine degrees and we're gonna translate it into radiance. And we do that by multiplying nine by pi divided by 180. And when we cross reduce, we find that our central angle will be pi divided by 20 radiant. Now, I think we have everything we need to be able to use this formula to find our arc length. So s is gonna equal our radius. So 6400 multiplied by our central angle of pi divided by 20. Again, I'm gonna cross reduce this. So 20 goes into 20 once, goes into 6403 120 times. So I know that as of right now, our arc length is 325 kilometers. However, that's not how they want it expressed. We want it expressed rounded to the nearest kilometer. So this means I'm gonna use a calculator and do 320 multiplied by pi. And when I do so I get 1005.3096 kilometers. And now to round that the nearest kilometer, we have 1005 kilometers. So that is our answer. That's the arc length or the distance between those two places and its answer choice. A have a nice day.

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N

Key Concepts

Great Circle Distance on a Sphere

Arc Length Calculation Using Central Angle

Conversion Between Degrees and Radians

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