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Math Help - Angles & bearings confusion

  1. #1
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    Angles & bearings confusion

    Hi,

    I've a similar problem to the one below but I don't quite understand how they arrived at the answer.

    "A boat travels from point A, to B, to C, then back to A.

    The bearing from A to B is S 27 degrees E
    The bearing from B to C is N 57 degrees W
    The bearing from C to A is N 16 degrees E

    If this route was in the form of a triangle, what would the three angles of the triangle be?"

    Answer
    A = 16+27 = 43 degrees
    B = 30 degrees
    C = 107 degrees

    I don't understand why 16+27 were added together to get A nor how B is 30. No matter what combination of subtracting or adding 90 degrees do I get 30.

    Any help is much appreciated, Geometry & Trig are my weak points in Maths.
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  2. #2
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    Re: Angles & bearings confusion

    Quote Originally Posted by dontpanic View Post
    Hi,

    I've a similar problem to the one below but I don't quite understand how they arrived at the answer.

    "A boat travels from point A, to B, to C, then back to A.

    The bearing from A to B is S 27 degrees E
    The bearing from B to C is N 57 degrees W
    The bearing from C to A is N 16 degrees E

    If this route was in the form of a triangle, what would the three angles of the triangle be?"

    Answer
    A = 16+27 = 43 degrees
    B = 30 degrees
    C = 107 degrees

    I don't understand why 16+27 were added together to get A nor how B is 30. No matter what combination of subtracting or adding 90 degrees do I get 30.

    Any help is much appreciated, Geometry & Trig are my weak points in Maths.
    The first step is ALWAYS to draw a diagram. From there you fill in whatever information you can from intuition, which is what I expect has happened here.
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  3. #3
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    Re: Angles & bearings confusion

    After drawing a few diagrams I get it now,57-27=30: 16+27=43. 27 is got from 90-63 and 16 from 90-74. Had to make two right angle triangles and work it out from there. Still don't like trig though.
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  4. #4
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    Re: Angles & bearings confusion

    Angles & bearings confusion-bearing.png

    The blue angles are alternate interior and therefore equal, and similarly for the red angles. By assumptions, blue angles are 16 and red angles are 27. This gives A = 16 + 27 = 43 and B = 57 - 27 = 30.

    Quote Originally Posted by dontpanic View Post
    Still don't like trig though.
    But isn't it cool to solve a problem that can realistically apply to real life?
    Thanks from Adikz
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