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Math Help - working out 'x' which is a side of a scalene inside a right-angle

  1. #1
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    working out 'x' which is a side of a scalene inside a right-angle


    Hello everybody.

    I was just wondering how one would calculate the length of x on the diagram above. The questions after this in my work are easier so I think I must be missing something easy here as well.

    it's not tan 50 100/x is it...?

    Any help would be brill, thank you.
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  2. #2
    Moo
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    Hello,

    If we name from up to down the points on the right side : A (summit), B, C, D (summit of right angle), what is x ? ;-)
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  3. #3
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    That's confused me... :s
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  4. #4
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    Hello, Jamie!

    [quote]
    Code:
        A o
          * *
        x *50*
          *     *
          *       *
        D o         *
          *   *       *
          *       *  10*
          *           *   * 
          *          30  * *
        C o * * * * * * * * * o B
                  100

    In right triangle DCB\!:\;\;\tan30^o \:=\:\frac{CD}{100}\quad\Rightarrow\quad CD \:=\:100\tan30^o\;\;{\color{blue}[1]}

    In right triangle ACB\!:\;\;\tan40^o \:=\:\frac{AC}{100}\quad\Rightarrow\quad AC \:=\:100\tan40^o\;\;{\color{blue}[2]}

    But AC \:=\:x + CD\quad\Rightarrow\quad x \:=\:AC - CD\;\;{\color{blue}[3]}


    Substitute [1] and [2] into [3]: . \boxed{x \;=\;100\tan40^o - 100\tan30^o}

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  5. #5
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    Brilliant, thank you for your help.
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