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Math Help - find distance

  1. #1
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    find distance

    i have a triangular plot of land through which a stream runs. the point B is due east of A and AB is 50m long. the bearing of C from A 026 degrees and the bearing of C from B is 328 degrees. calculate the distances AC and BC.

    could this problem be solved in a alternative way? if so, describe an alternative method.
    thanks
    jim
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  2. #2
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    Quote Originally Posted by jim49990 View Post
    i have a triangular plot of land through which a stream runs. the point B is due east of A and AB is 50m long. the bearing of C from A 026 degrees and the bearing of C from B is 328 degrees. calculate the distances AC and BC.

    could this problem be solved in a alternative way? if so, describe an alternative method.
    thanks
    jim
    If "bearing" means what I think it means, the interior angle of the triangle at A is 26 degrees and the interior angle of the triangle at B is 32 degrees. Is that right? Edit: No! The angles are 64 degrees and 58 degrees. In that case, I suggest you draw a line from C to a point D on the AB line chosen so that AB and CD are perpendicular.

    CD/AD=tan(26 degrees)
    CD/DB=tan(32 degrees)
    AD+DB=50 m

    Solve this for CD and use that CD=BC sin(32 degrees) and CD=AC sin(26 degrees).

    Alternative method? This is the only one I can think of right now.
    Last edited by Fredrik; December 10th 2006 at 06:27 AM.
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  3. #3
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    i dont think that is right

    i think the answer is 50m
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  4. #4
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    Hello, Jim!

    I hope you understand "bearings" . . .


    I have a triangular plot of land through which a stream runs.
    Point B is due east of A and AB is 50m long.
    The bearing of C from A is 26 and the bearing of C from B is 328.
    Calculate the distances AC and BC.
    Code:
                            C
                            *
                         *   *
          :           *  58  *   :
          :        *           *  :
          : 26 *               * :
          :  * 64           58 *:
        A * - - - - - - - - - - - * B
                      50

    Since \angle A = 64^o and \angle B = 58^o, then: \angle C = 58^o

    . . \Delta ABC is isosceles: AC = AB = 50 m.


    Law of Cosines: . BC^2\:=\:50^2 + 50^2 - 2(50)(50)\cos64^o\:=\:2808.144266

    Therefore: . BC \:=\:52.99192642\:\approx\:53 m.

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  5. #5
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    Apparently I got the angles of the triangle wrong. The method I suggested will get you the correct answer if you use the correct angles: 64 degrees and 58 degrees. So you can consider that the "alternative" method.
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  6. #6
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    many thanks

    thanks for that. the fact that there is a stream is irrelavant..
    jim
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