# Measuring Distances Using Lat / Long Coordinates (Math Problem Sample)

I had to calculate "Latitudes and longitude" problems provided in additional file

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Measuring Distances Using Lat/Long Coordinates

Part 1

Considering two landmark buildings, Andre in Tempe and Fort Lowell Museum in Tucson, from the google map, their coordinates approximated to the nearest 4 decimal places yield Andre (35.07850S, 150.68750E) and Fort Lowell Museum (32.22170N, 110.92640W).

Distance in Miles Using Pythagoras' Theorem. Acknowledging that to be able to use Pythagoras' Theorem, the obligate spheroid shape of the Earth will be assumed to be a plane surface. Hence, the sketch below would denote the two locations.

Now, the distances of the sides marked x and y must be obtained.

Normally, 10 = 180π ≈ 57.30 to the nearest four significant figures. Thus, converting both the latitudes and longitudes into radius,

Andre (35.07850S, 150.68750E) translates to (-0.6122, 2.6298) and Fort Lowell Museum (32.22170N, 110.92640W) translates to (0.5623, -1.9359)

Then:

Distance x = [ Cos (lat)× (longitudinal Difference)]

= [Cos (0.5623)× (1.9359 + 2.6298) × 3963 miles]

= 18092.99776 miles.

Similarly,

Distance y = [3963 (Latitudinal Difference)]

= [3963 (0.6122 + 0.5623) miles]

= 4654.5435 miles.

Recall that the differences were obtained by addition since they are on opposite sides of the GMT and Equator respectively.

Hence, from Pythagoras Theorem, the distance between the two buildings is given as:

Distance = (x2+y2) = (18092.99776 2+4654.5435 2)

= 18 681.9783 miles.

D

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