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Math Help - Law of Cosine Word Problems

  1. #1
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    Law of Cosine Word Problems

    A plane flies 810 miles from A to B with a bearing of N 75 degrees E. Then it flies 648 miles from B to C with a bearing of N 32 degrees E. Find the straight-line distance and bearing from C to A
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    Quote Originally Posted by jordangiscool View Post
    A plane flies 810 miles from A to B with a bearing of N 75 degrees E. Then it flies 648 miles from B to C with a bearing of N 32 degrees E. Find the straight-line distance and bearing from C to A
    The angle between AB and AC is 180 - 75 + 32 degrees
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  3. #3
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    Hello, jordangiscool!

    A plane flies 810 miles from A to B with a bearing of N 75 E.
    Then it flies 648 miles from B to C with a bearing of N 32 E.
    Find the straight-line distance and bearing from C to A
    Code:
                              Q     o C
                              :    *
                              :32* 
                              :  * 
                              : *
          P              105 |*
          :                   o B
          :               *   :
          :           *   75 :
          : 75   *           :
          :   *               R
        A o

    The plane flies from A to B\!:\;\;AB \,=\,810
    . . \angle PAB \,=\, 75^o \,=\,\angle ABR \quad\Rightarrow\quad \angle ABQ \,=\,105^o

    Then it flies from B to C\!:\;\;BC \,=\,648
    . . \angle QBC \,=\,32^o \quad\Rightarrow\quad \angle ABC \,=\,137^o


    Draw line segment AC.

    We have . \Delta ABC\!:\;\;AB = 810,\;BC = 648,\;\angle B = 137^o


    Law of Cosines: . AC^2 \;=\;AB^2 + BC^2 - 2(AB)(BC)\cos B

    Got it?

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