EXERCISE 3

Assume that City A and City B are located on the same meridian in the Northern hemisphere and that the earth is a sphere of radius 4000 mi. The latitudes of City A and City B are tex2html_wrap_inline109 and tex2html_wrap_inline111 , respectively.

(a)
Express the latitudes of City A and City B in decimal form.

(b)
Express the latitudes of City A and City B in radian form.

(c)
Find the distance between the two cities.

Solution: For parts (a) and (b), proceed as in Exercise 2:

align45

align54

Similarly, tex2html_wrap_inline113

(c) We use the Equation tex2html_wrap_inline115 , where s is the distance along the surface of the earth between the two cities, R is the radius of the earth, and tex2html_wrap_inline121 is the central angle between the two cities, that is, the difference in their latitudes. The distance between the two cities is then:

displaymath107

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Luis Valdez Sanchez
Tue Dec 3 15:03:31 MST 1996

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