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# Trigonometry question help?

Find the distance between Omaha, NE and Tulsa, OK, which lie on the same longitude. The latitude of Omaha is 41.25°N and the latitude of Tulsa is 36.15°N. Use a radius of 3960 miles for the Earth and round your solution to two decimal places.

### 3 Answers

- lenpol7Lv 71 month ago
Angular difference is 41.25 - 36.15 = 5.1 degrees.

Knowing the radius to be 3960 miles. then the Arc length is

Arc = (5.1/360)2 pi (3960)

Arc = (5.1/180) (3.141592)(3960)

Arc = 352.4866... miles. Is the distance between Tulsa and Omaha.

- Bill-MLv 71 month ago
That is not a Trigonometry Question. It is a Latitude Distance problem.

Lines of Latitude (Whole Degrees) are 60 Nautical Miles apart.

41 Degrees 25 Minutes MINUS 36 Degrees 15 Minutes is 5 Degrees 10 Minutes

Convert 10 Minutes to a 10th of a Degree.

Now you have 5.1667 Degrees difference between the two cities.

5.1667 times 60 = 310 Nautical Miles

- billrussell42Lv 71 month ago
straight line distance (which cuts thru the earth surface) or distance along a great circle? assume the latter, which would be the arc of a circle of radius of 3960 mi and angle of 41.25° – 36.15°

circumference = 2π3960

arc length = (2π3960)(41.25° – 36.15°)/360º = 352 mi

straight line distance would be a bit smaller.

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