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Math Help - Basic trig, solving side of triangle

  1. #1
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    Basic trig, solving side of triangle

    A ship is headed east @ 15 MPH.
    There is a tide North-10 degrees-East @ 5 MPH.
    Find the course and speed of the ship.
    Here is what I got so far:



    But the solution 15.7875 MPH is incorrect so undoubtedly my angle would come out incorrect too.

    Where have I gone wrong?
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  2. #2
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    Re: Basic trig, solving side of triangle

    You've changed the tide so that it is in the northerly direction only. It will have an easterly component as well.
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    Re: Basic trig, solving side of triangle

    Oh, I see what I did wrong now. I put right angles where they don't exist:

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    Re: Basic trig, solving side of triangle

    Quote Originally Posted by daigo View Post
    Oh, I see what I did wrong now. I put right angles where they don't exist:

    Your sketch looks a little bit weird to me.

    Don't forget the addition of 2 vectors is represented by a parallelogram.
    Attached Thumbnails Attached Thumbnails Basic trig, solving side of triangle-shipscoursecorrected.png  
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    Re: Basic trig, solving side of triangle

    I've been told that but I don't understand why so I am trying to go through it right now to see if I can get why the new course is adding two vectors.
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    Re: Basic trig, solving side of triangle

    You have two options.

    1. You can leave the tide as it is and add it vectorially to the velocity of the boat. To do that form a parallelogram from the vectors representing the tide and the speed and direction of the boat. (It will be like your last diagram except that the line at the top will be horizontal.) Then you have to calculate the length of the long diagonal using the cosine rule, and also the angle it makes with the northern direction.

    2. Alternatively, split the tide into two components 5cos(10) in a northerly direction and 5cos(80) in an easterly direction. (The two together will be equivalent to the actual tide.) That will mean that effectively the boats speed in the easterly direction will be 15+5cos(80) not the 15 that you had for your first attempt. Complete the rectangle and you can use Pythagoras to calculate the length of the diagonal.

    Try doing it both ways and show that you get the same result.
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