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Math Help - trignometry

  1. #1
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    trignometry

    please solve this sum for me---
    an aeroplane sets off from G on a bearing of 024 degrees towards H a point 250 km away .At H it changes course and heads towards J on a bearing of 055 degrees and a distance of 180 km away.
    1)How far is H to the north of G.
    2)How far is H to the east of G.
    3)How far is J to the north of H.
    4)How far is J to the east of H.
    5)What is the shortest distance between G and J.
    6)What is the bearing of G from J.
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  2. #2
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    Hello, dolly kohli!

    Did you make a sketch?
    I'll get you started on this one . . .


    An airplane sets off from G on a bearing of 024 degrees
    towards H a point 250 km away. At H it heads towards J
    on a bearing of 055 degrees and a distance of 180 km away.
    Code:
                  Q         o J
                  :   180 * :
                  :     *   :
                  :55*     :
                  : * 35   :
          P     H o - - - - + C
          :      /:         :
          :  240/ :         :
          :    /  :         :
          :24/   :         :
          :  /    :         :
          : /     :         :
          :/ 66  :         :
        G o - - - + - - - - +
                  A         B

    \angle PGH = 24^o \quad\Rightarrow\quad \angle HGA = 66^o \quad\Rightarrow\quad \angle GHA = 24^o

    \angle QHJ = 55^o \quad\Rightarrow\quad \angle JHC = 35^o

    GH = 240,\; HJ = 180



    1)How far is H to the north of G ?
    We want HA.

    In \Delta HAG\!:\;\;\sin66^o = \frac{HA}{240} \quad\Rightarrow\quad HA \:=\:240\sin66^o \:\approx\: 219.25



    2)How far is H to the east of G ?
    We want GA.

    In \Delta HAG\!:\;\;\cos66^o = \frac{GA}{240} \quad\Rightarrow\quad GA \:=\:240\cos66^o \:\approx\:97.62



    3) How far is J to the north of H ?
    We want JC.

    In \Delta JCH\!:\;\;\sin35^o = \frac{JHC}{180} \quad\Rightarrow\quad JC \:=\:180\sin35^o \:\approx\:103.24



    Are you getting the idea?

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  3. #3
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    thanku for ur help but i wanted the last three answers because first 3 even i got correct
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  4. #4
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    Quote Originally Posted by dolly kohli View Post
    thanku for ur help but i wanted the last three answers because first 3 even i got correct
    It would have saved a lot of time if you'd said that in your original post and given the answers
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