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20 June, 14:06

Two sailboats leave a harbor in the bahamas at the same time. the first sails at 23 mph in a direction 330°. the second sails at 34 mph in a direction 190°. assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats?

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  1. 20 June, 15:10
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    First, let us calculate the total distance that each have taken after 2 hours.

    Let’s say that:

    A = sailboat which sails at 23 mph in a direction 330°

    B = sailboat which sails at 34 mph in a direction 190°

    Calculating for distances:

    dA = 23 mph (2 hours) = 46 miles

    dB = 34 mph (2 hours) = 68 miles

    Imagining a Cartesian coordinate, the angle θ between the two sailboats is simply the difference:

    θ = 330° - 190°

    θ = 140°

    We know that from the law of cosines:

    c^2 = a^2 + b^2 - 2 a*b*cos θ

    Therefore the distance between the two after 2 hours, C, is:

    C^2 = 46^2 + 68^2 - 2 (46) (68) cos (140)

    C = 107.39 miles
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