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Starting from one oasis, a camel walks 25km in a direction 30 degrees south of west and then walks 30km toward the north to a second oasis. What distance separates the two oases?

  • maths -

    I made a quick sketch and found the angle between the two paths to be 60°
    So it becomes a simple Cosine Law

    x^2 = 25^2 + 30^2 - 2(25)(30)cos60
    = 775
    x = √775 = 27.84 appr.

  • maths -

    Take x as east, and y as north, and the starting position as (0,0).

    The coordinates of the first stop are
    (-25cos(30°), -25sin(30°)
    The second stop is simply 30km towards +y, or
    (-25cos(30°), 30-25sin(30°)

    Use Pythagoras theorem to calculate the distance from the original point (0,0).

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