Geometry (clue: use geometry of circles, not a map or globe, in figuring these o

Question

Geometry (clue: use geometry of circles, not a map or globe, in figuring these out - the diagrams below are only to help you think geometrically): List the latitude and longitude coordinates (global position) for a point on earth: this point is halfway between the Equator and North Pole, and one-third of the way around the world eastward from Greenwich. Pinpoint the global position for the spot where you would be if you were exactly half-way (180 degree) around the world from Duluth, which lies at 47 degree N and 92 degree W. Clue: you need to do latitude and longitude separately. The USA's northern boundary (excluding Alaska and Minnesot's "Chimney") is 49 degree N Latitude. The "Southernmost Point" in the U.S. (in Key West) is at 24 degree 30' N. The question - how tall in miles is the continental USA?

Explanation / Answer

11 a) Here the the position on the ground is on the Northern hemisphere between the Equator and the Northern Pole i.e., 45o N and along the Eastern part from the Greenwich i.e., 2/3 of 180o which comes to be 120o E. So the coordinates is coming to be

Latitude- 45o N

Longitude- 120o E and this point on the ground is coming to be in China at JARUD.

b) The given coordinates at Duluth is 47o N and 90o W so its anti pods would be

I) 47o N and 90o E

II) 45o S and 90o W.

Above result can be calculated by using formula as (, ± 180)

where,

= latitude of the given location

= Longitude of the given location

This will give two different values when considering longitude and latitude individually.

12) In this question only the values of the latitude are given so we’ll assume the longitude are same so this can be calculated by this formula

Distance = R * arccos (sin(latA) * sin(latB) + cos(latA) * cos(latB) * cos(lonA-lonB))

since the longitude is same the above formula ‘ll reduce to

Distance = R * arccos (sin(latA) * sin(latB)

where the value of the R= 6372.795477598 km,

Distance= 6372.795477598* arccos {(sin(49o)* sin(24.5o)}

Distance= 457321.447 km

so US is almost 457321.447 km long.

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