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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…

Dallas: 32.786°

Omaha: 41.262°

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.

### 2 Answers

- 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.