Find the distance between Bowling Green, KY and Hiawatha National Forest?

Question

Solve the following Math problem:

Bowling Green, KY, with the latitude 36.98 degrees N and longitude 86.5 degrees W. measure the distance from this place to that site in Hiawatha National Forest, in the Upper Peninsula of Michigan, with the same longitude and latitude 46.21 degrees N. Considering the radius of the earth to be 6371km.

Find the distance between the places on a straight path, in km.

Answer 1

To find the distance between Bowling Green, KY and Hiawatha National Forest implement the following steps.

Convert Degrees in the math problem to Radians

Use the formula: Radians = Degrees x (pi divided by 180) Notes: pi /180, pi =3.141592654, x (multiply)

Bowling Green:

Latitude: 36.98 degrees --- 36.98 x (pi/180) = 36.98 x 3.141592654 divide by 180 =116.1760963/180=.6454227574 radians round answer off as specified 0.645 radians

Longitude: -86.5 degrees W -86.5 x (pi/180) = -86.5 x (3.141592654 divided by 180) =

-86.5 x .0174532925 = -1.509709803 radians round off answer as specified -1.51 radians

Note: When expressing longitude coordinates negative degrees represent the western hemisphere.

Hiawatha National Forest:

Latitude: 46.21 degrees N 46.21 x (pi/180) = 46.21 x (3.141592654 divided by 180) =

46.21 x .0174532925 = .8065166473 radians round off answer as specified .807 radians

Longitude: -86.5 degrees W -86.5 x (pi/180) = -86.5 x (3.141592654 divided by 180) =

-86.5 x .0174532925 = -1.509709803 radians round off answer as specified -1.51 radians

Note: When expressing longitude coordinates negative degrees represent the western hemisphere.

Calculate the Differences (Δ) of Bowling Green and Hiawatha latitude and longitude:

Bowling Latitude = 0.645 radians Hiawatha Latitude = 0.807 radians

Δ latitude = 0.807 - 0.645 = 0.162 radians

Bowling Longitude = -1.51 radians Hiawatha Latitude -1.51 radians

Δ Longitude = -1.51 - (-1.51) = 0 radians

Use the Distance Formula: Distance = R x c

Note: R= radius of Earth = 6371 kilo meters (km)

R represents the radius of a circular path and c represents the circumference of the travel locations.

Calculate Distance = d = R x c R = 6371 km c = Δ latitude = 0.162 radians

d = 6371 x 0.162 = 1032.102 km ( round off answer as specified )

so the distance from Bowling Green to Hiawatha National Forest is about 1032 km

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.