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Math Help - Law of Sines

  1. #1
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    Law of Sines

    The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 degrees East, and the two towers are 30 km apart. A fire spotted by rangers in each tower has a bearing of N 80 degrees East from Pine Knob and S 70 degrees E from Colt Station. Find the distance of the fire from each tower.
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  2. #2
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    Re: Law of Sines

    Hey alexthesauceboss.

    Are the two triangles right angled ones?
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  3. #3
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    Re: Law of Sines

    Hello, alexthesauceboss!

    \text{The bearing from the Pine Knob fire tower to the Colt Station fire tower is }N\,65^o\,E.
    \text{The two towers are 30 km apart. }\,\text{A fire spotted by rangers in each tower.}
    \text{It has a bearing of }N\,80^o\,E\text{ from Pine Knob and }S\,70^o\,E\text{ from Colt Station.}
    \text{Find the distance of the fire from each tower.}

    The diagram looks like this:
    Code:
                              C
                              o
                            * : *
          N               *65o:70o*
          :             *     :     *
          :        30 *       :       *
          :         *         :     30o o F
          :       *           :   *
          : 65o *           * :
          :   * 15o   *       S
          : *   *
        P o
    Pine Knob is at P, Colt Station is at C.
    \angle N\!PC = 65^o,\;PC = 30.

    The fire is at F.
    \angle N\!PF = 80^o \quad\Rightarrow\quad \angle CPF = 15^o.
    \angle FCS = 70^o \quad\Rightarrow\quad \angle PCF = 135^o \quad\Rightarrow\quad \angle F = 30^o


    Law of Sines:

    . . \frac{CF}{\sin15^o} \:=\:\frac{30}{\sin30^o}

    . . \frac{PF}{\sin135^o} \:=\:\frac{30}{\sin30^o}


    Go for it!
    Thanks from alexthesauceboss
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