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Math Help - Law of Sines and Cosine problem help...I'm stumped.

  1. #1
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    Law of Sines and Cosine problem help...I'm stumped.

    http://img100.imageshack.us/img100/6232/dscn1765mw2.jpg

    A 125-ft tower is located on the side of a mountain that is inclined 32(degrees) to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55; ft downhill from the base of the tower. Find the shortest length of the wire needed.

    I plug some things into the law of cosines and I get to
    3025 = 15625b^2 - 250b*cos(58)

    For the love of god help, this is due tomorrow -_-
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  2. #2
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    Hello, MmmmSteak!

    A 125-ft tower is located on the side of a mountain that is inclined 32 to the horizontal.
    A guy wire is to be attached to the top of the tower and anchored at a point 55 ft
    downhill from the base of the tower.
    Find the shortest length of the wire needed.
    Code:
                              o A
                            * |
                          *   |
                        *     |125
                      *       |
                  x *    122 o B
                  *       *58|
                *     *       |
              *   * 55        |
            * * 32           |
        C o - - - - - - - - - o D

    The tower is: . AB = 125
    The guy wire is: . x = AC
    And: . BC = 55

    \angle BCD = 32^o
    . . Then: . \angle CBD = 58^o
    . . Hence: . \angle ABC = 122^o


    Law of Cosines: . x^2 \;=\;125^2 + 55^2 - 2(125)(55)\cos122^o \;=\;25936.38988


    Therefore: . x \;=\;161.0477876 \;\approx\;\boxed{161\text{ ft}}

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  3. #3
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    I actually just finished working this out (with help of a friend) when I got your reply, and this was my answer. This is so incredibly difficult...

    I have two more.

    5. Write the trigonomic expression (cot[x])/(csc[x]-sin[x]) in terms of sine and cosine, and simplify.
    8. Use the formulas for lowering powers to rewrite the expression cos^4[x] in terms of the first power of cosine.

    I got something on #5, but it wasn't right so I scrapped it. I don't know what #8 is talking about.

    Thank you so very, very much for you help.
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