Question

Pittsburgh, Pennsylvania, and Buffalo, New York, lie approximately on the same meridian. Pittsburgh has a latitude of 40.5° N, and Buffalo has a latitude of 42.9° N. Find the distance between these two cities. (The radius of the earth is 3960 mi. Round your answer to the nearest mile.)

Answer 1

Answer:

  166 mi

Step-by-step explanation:

The length of an arc of a circle is the product of the radius and central angle measure in radians. For this problem, the central angle is the difference in latitude. The degree measure is converted to radian measure by multiplying by π/180°.

  distance = (42.9° -40.5°)(π/180°)(3960 mi) ≈ 166 mi

The distance between the two cities is about 166 miles.

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You can get an answer good within 0.1% by using 60 nautical miles per degree. The 2.4° difference in latitude gives 144 nautical miles, which translates to 166 statute miles, so gives the same answer.