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Math Help - [SOLVED] Using the sine rule.

  1. #1
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    [SOLVED] Using the sine rule.

    Town B is 6 km, on a bearing of 020, from town A. Town C is located on a bearing of 055 from town A and on a bearing of 120 from town B. Work out the distance of town C from (a) town A and (b) town B.
    Can someone show me how the diagram is suppose to look like and how to solve this . As I don't really understand how to work with bearings.

    thanks!
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  2. #2
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    Hello, Tweety!

    Town B is 6 km, on a bearing of 020, from town A.
    Town C is located on a bearing of 055 from town A and on a bearing of 120 from town B.
    Work out the distance of town C from (a) town A and (b) town B.

    Bearings are measured clockwise from North.
    Code:
                    Q
                    :
                    :
                  B o 120
          P        /: *
          |       / :60*
          |      /  :     *
          |     /20:       *
          |    /    :     70 o C
          |20/     :     *
          |  /      : *
          | / 30 * :
          |/  *     :
        A o         R

    \angle PAB \:=\: 20^o\:=\:\angle ABR,\:AB = 6\text{ km}

    \angle PAC \:=\:50^o \quad\Rightarrow\quad \angle BAC \:=\:30^o

    \angle QBC \:=\:120^o \quad\Rightarrow\quad \angle CBR \:=\:60^o\quad\Rightarrow\quad \angle ABC \:=\:80^o


    In \Delta ABC\!:\;\;\frac{AC}{\sin80^o} \:=\:\frac{6}{\sin70^o} \quad\Rightarrow\quad AC \:=\:\frac{6\sin80^o}{\sin70^o} \:\approx\:6.3\text{ km}

    . . . . . . . . \frac{BC}{\sin30^o} \:=\:\frac{6}{\sin70^o} \quad\Rightarrow\quad BC \:=\:\frac{6\sin30^o}{\sin70^o} \:\approx\:3.2\text{ km}

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  3. #3
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    edit Soroban's excellent graphic so that angle BAC = 35 instead of 30 and angle BCA = 65 instead of 70.

    fix that also in the law of sines equations and you'll be fine.
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  4. #4
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    Quote Originally Posted by Tweety View Post
    Can someone show me how the diagram is suppose to look like and how to solve this . As I don't really understand how to work with bearings.

    thanks!
    Bearings are the angles measured from North to clockwise direction. Please see attached diagram.
    Attached Thumbnails Attached Thumbnails [SOLVED] Using the sine rule.-p1.jpg  
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