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Math Help - Bearing problem: Sine and cosine

  1. #1
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    Exclamation Bearing problem: Sine and cosine

    Two ship leave a port at the same time. The first ship sails on a course of 35 at 15 knots, while the second ship sails on a course of 125 at 20 knots. Find after 2 hours (a)distance between the ship (b)the bearing from the first ship to the second (c) and the bearing from the second ship to the first.


    Hoping for answers -.-
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  2. #2
    Senior Member Paze's Avatar
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    Re: Bearing problem: Sine and cosine

    Well if the first ship leaves at a 35 degree angle relevant to the port and the 2nd ship leaves at a 125 degree angle relevant to the port, then the angle on the triangle which the ships form, becomes 90 degrees (125-35). The distance after 2 hours on the first ship is 30 knots and the 2nd ship has sailed 40 knots.

    Since you have a right triangle, you can now use the Pythagorean theorem to show that the distance between the ships is \sqrt{30^2+40^2}

    Now you can get the bearings or the other angles of the triangle by using (arc)trig functions.

    tan^{-1}\left(\frac{40}{30}\right)=53.13. Now we can use: 180-53.13-90=36.87.
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  3. #3
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    Re: Bearing problem: Sine and cosine

    That was quick! Thank you very much I understood your solution completely Never thought i would get a reply so fast
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