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  1. #1
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    Arrow math help

    hi I need major help in trig there is only 4 questions so yeah any help would be VERY helpful to me! thanks!
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  2. #2
    Super Member

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    Hello, Justin!

    Here's #1 . . .


    In the triangle shown,  AC = 194 cm.
    What is the length of BD to the nearest cm?
    Code:
                                              * D
                                        *   * |
                                  *       *45|
                            *           *     |
                      *               *       |
                * 15             B *         |
        A *-----------------------*-----------* C
          : - - - - - - - 194 - - - - - - - - :

    In right triangle DCA\!:\;\;\tan 15^o \:=\:\frac{CD}{AC}

    . . Then: . CD \:=\:AC\tan15^o \:=\:194\cdot\tan15^o\quad\Rightarrow\quad CD \:\approx\:51.98


    In right triangle DCB\!:\;\;\cos45^o = \frac{CD}{BD}\quad\Rightarrow\quad BD \:=\:\frac{CD}{\cos45^o}

    . . Therefore: . BD \:=\:\frac{51.98}{\cos45^o} \:=\:73.51082097\quad\Rightarrow\quad\boxed{BD \:\approx\: 74\text{ cm}}

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