Mathematics

May I have some help with this question? I'm not sure how to solve it.
A boat leaves Kingston and heads due east for 25 km. At the same time, a second boat travels in a direction 30° south of east from Kingston for 15 km. How far apart are the boats at this moment when they reach their destinations?
Thank you!

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  1. After you make your sketch and let x km be the distance between them, you will see that
    x^2 = 25^2 + 15^2 - 2(25)(15)cos30°
    ....

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    Reiny
  2. Thanks!

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  3. All angles are measured CW from +y-axis.
    KA = 25km[90o].
    AK = 25km[90+180].
    KB = 15km[120o].

    AB = AK+KB = 25[270o]+15[120o]
    AB = (25*sin270+15*sin120)+(25*cos270+15*cos120)i
    AB = -12-7.5i = 14.2km[58o]W. of S. = 14.2km[238o] = distance between the boats.

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