Question

In: Advanced Math

The latitude of any location on Earth is the angle formed by the two rays down...

The latitude of any location on Earth is the angle formed by the two rays down from the center of Earth to the location and to the equator. The ray through the location is the initial ray. Use 3960 miles as the radius of the Earth. Suppose City A is due north of City B. Find the distance between City A (north lattitude 41 degrees 17' N) and City B (latitude 32 degrees 47')



the distance between City A and City B is approximately__ miles

Solutions

Expert Solution

The positioning of the two cities can be simplified in drawing as shown below :

A and B show the position of cities A and B respectively with respect to equator.

Now, the distance between the cities A and B is the length of arc AB. This can be computed as

AB = EA - EB

The formula for length of an arc is given as

length of arc = radius x angle of arc in radians

The formula for converting angle to radians is given as :

Converting latitude of city A into radians,

Thus, the length of arc EA = 3960 * 0.72053 = 2853.299 miles

Converting latitude of city B into radians,

Thus, the length of arc EA = 3960 * 0.57218 = 2265.8213 miles

Now, the length of arc AB = 2853.299 - 2265.8213 = 587.477 miles

Thus the distance between the cities A and B is 587.477 miles

Colby Messinger answered 1 year ago
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