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Math Help - [SOLVED] Law of Sines

  1. #1
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    [SOLVED] Law of Sines

    Need help with the following problem involving the Law of Sines: A corner of a park occupies a triangular area that faces two streets that meet at an angle of 85 degrees. The sides of the area facing the street are each 60 feet in length. A landscaper wants to plant flowers around the edges of the triangular area. Find the perimeter of the triangular area. [The answer is 201.1 feet.]

    Thanks.

    Garrett
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  2. #2
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    Hello, Garrett!

    Need help with the following problem involving the Law of Sines:
    A corner of a park occupies a triangular area that faces two streets
    that meet at an angle of 85 degrees.
    The sides of the area facing the street are each 60 feet in length.
    A landscaper wants to plant flowers around the edges of the triangular area.
    Find the perimeter of the triangular area.
    [The answer is 201.1 feet.]
    Code:
                          A
                          *
                        *   *
                      *  85  *
               60   *           *  60
                  *               *
                *                   *
              *                       *
            *  47.5             47.5  *
        B *   *   *   *   *   *   *   *   * C
                          x
    If we must use the Law of Sines, here we go . . .

    Triangle ABC is isoceles: AB = AC
    . . Hence: . \angle B = \angle C

    Since: . A + B + C \:=\:180^o, we have: . \angle B \,= \,\angle C \,= \,47.5^o


    Law of Sines: . \frac{x}{\sin85^o} \:=\:\frac{60}{\sin47.5^o} \quad\Rightarrow\quad x \:=\:\frac{60\sin85^o}{\sin47.5^o} \:=\:81.07082...

    . . Hence: . x\:\approx\:81.1 feet.


    Therefore: . \text{Perimeter} \:=\:60 + 60 + 81.1 \:=\:201.1\text{ feet}

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  3. #3
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    Thank you Soroban.

    I had drawn an incorrect diagram.

    Garrett

    Quote Originally Posted by garrett88 View Post
    Need help with the following problem involving the Law of Sines: A corner of a park occupies a triangular area that faces two streets that meet at an angle of 85 degrees. The sides of the area facing the street are each 60 feet in length. A landscaper wants to plant flowers around the edges of the triangular area. Find the perimeter of the triangular area. [The answer is 201.1 feet.]

    Thanks.

    Garrett
    Follow Math Help Forum on Facebook and Google+

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