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Smalltown, latitude 53.6 degrees N, lies directly north of Bigville, latitude 38.6 degrees N. Give the distance between the two cities. (Hint: The earth's radius is about 3,960 miles.)

This is a question similar to what will be on my test tomorrow. I'd really appreciate the help on how to figure this out.

The answer is 330 Pi or 1,036.7 miles.

  • Trigonometry -

    draw a 'great circle'
    the two towns form a sector with an angle
    of 15º (53.6-38.6 = 15)
    15º = pi/12 radians

    you want the arclength of that sector
    arclength = radius x angle
    = 3960(pi/12) = 330pi

  • Trigonometry -


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