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Trig homework help please, finding distance between cities?
Assume that the earth is a sphere of radius 4000 miles and that the cities are on the same longitude.
Dallas, TX has a latitude of 32°47'9"
Omaha, Nebraska is 41°15'42"
I converted each city into decimal form and I got…
What do I do from here? Clear steps would be lovely since my book doesn't explain how to do these types of problems.
And, I'm not lazy, I just don't have a clue of what to do from here.
- SBLv 69 years agoFavorite Answer
You need to calculate the arc length of a 4000 mile raduis arc with an angle equal to the difference between the lattitudes of the two cities
The angle is 41.262 - 32.786 = 8.476 deg
The arc length (d) is then found by setting up a ratio between the arc length and the circuference of the earth
2*pi*r / 360 = d / 8.476
d=2*pi*4000*8.476/360 = 591.74
And if you check the flight distance from DFW to OMA airports you get 583 miles. So the above number is at least reasonable.
Hope this helps.